A Large-Scale Study of the Twitter Follower Network to Characterize the Spread of Prescription Drug Abuse Tweets
Ryan Sequeira, Avijit Gayen, Niloy Ganguly, Sourav Kumar Dandapat, Joydeep Chandra
aa r X i v : . [ c s . S I] F e b This is a preprint version. Please cite the work by using the reference on https://ieeexplore.ieee.org/document/8863642R. Sequeira, A. Gayen, N. Ganguly, S. K. Dandapat and J. Chandra, ”A Large-Scale Study of the Twitter Follower Network to Characterize theSpread of Prescription Drug Abuse Tweets,” in IEEE Transactions on Computational Social Systems, vol. 6, no. 6, pp. 1232-1244, Dec. 2019, doi:10.1109/TCSS.2019.2943238.
A Large Scale Study of the Twitter FollowerNetwork to Characterize the Spread of PrescriptionDrug Abuse Tweets
Ryan Sequeira, Avijit Gayen, Niloy Ganguly, Sourav Kumar Dandapat, Joydeep Chandra
Abstract —In this paper, we perform a large-scale study of theTwitter follower network, involving around . million userswho justify drug abuse, to characterize the spreading of drugabuse tweets across the network. Our observations reveal theexistence of a very large giant component involving of theseusers with dense local connectivity that facilitates the spreadingof such messages. We further identify active cascades over thenetwork and observe that cascades of drug abuse tweets getspread over a long distance through the engagement of severalclosely connected groups of users. Moreover, our observationsalso reveal a collective phenomenon, involving a large set of activefringe nodes (with a small number of follower and following)along with a small set of well-connected non-fringe nodes thatwork together towards such spread, thus potentially complicatingthe process of arresting such cascades. Further, we discoveredthat the engagement of the users with respect to certain drugslike Vicodin, Percocet and OxyContin, that were observed to bemost mentioned in Twitter, is instantaneous. On the other handfor drugs like Lortab, that found lesser mentions, the engagementprobability becomes high with increasing exposure to such tweets,thereby indicating that drug abusers engaged on Twitter remainvulnerable to adopting newer drugs, aggravating the problemfurther. Index Terms —Social computing, Twitter, Information retrieval,Biomedical informatics
I. I
NTRODUCTION T HE enormous popularity of social media like Twittermakes it suitable as an advertisement platform for pro-moting drug-abuse. Keeping in view the spread and impact ofdrug-abuse (there is an estimated count of , prematuredrug-related deaths ), and the limitations of traditional “pre-scription drug monitoring programs” (PDMPs) in understatingthe severity of this issue [1] there is a need to have adeeper understanding of how social media is playing a rolein promoting the drug menace.We focus our attention on the Twitter platform, that isone of the key media used to spread information related todrugs. Several background works exist that have highlightedthe role of Twitter in the sale of illicit drugs [2] and thepromotion of drug-abuse [3]. Possible surveillance strategiesfor identifying such retailers and drug-abusers have also beenwell explored [4]. However, an important aspect that needsto be carefully investigated is the networked effect of Twitterthat may amplify the spread of drug-abuse tweets among users.Preliminary studies of Twitter users in [5] reveal the existence of drug-related social circles (densely connected neighbor setof a user) around certain active users who tweet frequently,mentioning the different effects that specific drugs produce.Although it is not completely clear whether such active circlescan influence non drug-abusers towards abuse, however, fromconcepts like the “ uses and gratification theory ” and “ HealthCommunication Media Choice ” (HCMC) model [6], it can beargued that such discussions that glorify drug-abuse are likelyto engage users who justify drug-abuse in further deliberationsto satisfy their communication needs. Consequently, cascadesof user engagement, if formed through such discussions, wouldvolume up as social advertisements that would downplaythe ill effects of drug-abuse and may influence vulnerableusers towards such practice. In this paper, we discover andcharacterize such cascades over the Twitter follower network,where users participate in discussions that treat drug-abusepositively.To identify these cascades, we propose a technique thatuncovers around . million unique users who were engagedin either self-reporting or promoting prescription drug-abusethrough tweets. The enormity of this number reflects the hugerole being played by social media in promoting prescriptiondrug-abuse on Twitter. However, the dynamics of these cas-cades are mainly driven by the users’ engagement behavior,as well as the underlying structure of the follower network.Hence in our study, we follow a principled approach by firstinvestigating the underlying follower network of these uniqueusers and subsequently the characteristics of these users interms of their engagement behavior and positional importancein the network, before finally studying the key features ofthe cascades. The follower relation among these users is usedto create a network with directed edges. Investigation revealsthat this network is almost entirely connected with around . of the nodes being in the largest strongly connectedcomponent. We also observe very high reciprocity of thelinks in the network. All these network properties indicatethe network structure is amenable to the large-scale spread ofinformation. The spread, however, depends on the activenessof the users (frequency of engagement) as well as their positionin the network. We assessed the activeness of the users andfound that around one-fourth of the users are active. Moreover,the reach of these active nodes is considerable, as they covera substantial part of the network.From the detailed study of the nature of the network andits participating users, it is clear that a structure susceptibleto facilitate the formation of cascades exist. We discover Copyright © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or futuremedia, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution toservers or lists, or reuse of any copyrighted component of this work in other works. DOI: 10.1109/TCSS.2019.2943238. around , cascades, some of them with sizes reachingto thousands and extending over several hops. The networkstudy of such cascades reveals high structural virality, i.e.the cascades are not driven by a single important node,which in turn makes them difficult to control. Further, thenetwork among the nodes participating in each cascade exhibitsignificantly high clustering coefficient and reciprocity intheir follower relationships. All these observations provide astrong evidence that drug-abuse tweets traverse through severalgroups of closely connected users. Moreover, the study ofthe characteristics of these users reveals equally importantcontributions, irrespective of their position and activeness,in the spreading process. The phenomenon indicates thatorganic collaboration among a large set of nodes is largelyresponsible for the emergence of a cascade; thus it may bedifficult to control the cascades by eliminating a few targetednodes. Finally, guided by the metrics associated with socialcontagion processes [7] (discussed in detail later), we findthat users engage (through tweets or retweets) differentlywhen exposed to drug-abuse tweets with different drug names.On exposure to tweets with highly mentioned drug nameslike Vicodin, Percocet and OxyContin, the engagement isinstantaneous, whereas for less popular drugs like Lortab thechances of engagement increase with increasing exposure tosuch mentions. This signifies that drug-abusers engaged onTwitter remain at risk of adopting newer drug types to whichthey are continually exposed through Twitter discussions.The rest of the paper is organized as follows. In the nextsection, we highlight the related works. In section III, we de-scribe the detailed dataset used in our work. In this section, weexplain the data collection process as well as the classificationmethod to identify the drug-abuse tweets. In section IV, wedescribe the follower network formation method and furtherdetail its network characteristics. We subsequently discussthe user characteristics in section V. The details about thespreading pattern of the tweets across the follower networkare outlined in section VI. Finally, we summarize our findingsin section VII. II. R ELATED W ORK
A plethora of recent work uses social media to gatherinformation and in turn, provide solutions to various issuesrelated to health. For example, social media has played anvital role in providing rich information for inferring mentalhealth conditions (especially depression [8], mood instabil-ities [9], suicidal risks [10] and the effects of psychiatricmedication [11]), as well as lifestyle-related conditions likeovereating, alcoholism and smoking [12]. Technological ap-proaches are being leveraged for addressing critical issues likethe early prediction of such diseases [8], increased supportand service engagement [13] and a decrease in the durationof untreated disorders [14]. These works provide a directionto the critical issues, concerning the psychological problems(including the drug-abuse problem), that require immediateattention.Recently, prescription drug-abuse is receiving increasingattention due to its significant spread and the casualties in-volved [15], [16]. Majority of these work are directed towards identifying content on social media that reveal drug-abusebehavior of the users. Such techniques include both supervisedclassification [17]–[20] as well as unsupervised methods [15],[21] for identifying drug-abuse tweets from the tweet stream.Complementary to the problem of drug-abuse detection, worksbased on identifying alternative opioid recovery treatments onsocial media also exist [22]. Such data can be leveraged to gaininsights about the microscopic behavior of the correspondingusers and their role in spreading drug-abuse tweets in thenetwork, although only a few works have attempted to doso [2], [5]. One of the primary goals of this paper is to worktowards these objectives.In [5], the authors pointed out the influence of neighbors(network effect) on the participation of users in discussionsrelated to drug-abuse. They observed the presence of socialcircles in which active users (users who frequently discuss theabuse of specific drugs on Twitter) are likely to be surroundedby users who also participate in similar discussions, exhibitinga high content correlation among them. While this workprovides preliminary insights about the tweeting behavioramong these participating users, revealing the existence of apossible group phenomenon; to the best of our knowledge,no other work has attempted to take a closer look into thespread of drug-abuse discussions on social media platforms.However, the study of the propagation of different tweetcontent to understand human behavior has been a focus areaacross various topical domains. One of the earlier works oninformation flow on Twitter [23] showed the presence of afew elite users in Twitter who generate a majority of thecontent that is consumed by ordinary users. Several otherworks have also investigated the user characteristics and therole of influential users in information propagation acrosssocial networks [24], [25]. Subsequent empirical works haveexamined several other factors like the underlying networkof the users [26]–[28], the user characteristics [29]–[31] therole of content [32], [33] and even the role of the underlyingdiffusion protocols [34] in such propagation. Selected workshave investigated the effects of both users and content ininformation propagation [35], [36]. Since the dynamics ofinformation propagation across networks vary with topics andcontent, this motivates the need to investigate the spreadingbehavior in the context of drug-abuse tweets by inspecting thecascades of user engagement, the role of the network and theuser characteristics in the spreading process.Spreading of various social behaviors has been investigatedin several works, like the cessation of smoking [37], onlinesharing [38], and political controversies [7]. These works high-light the importance of collective dynamics, often modeledthrough a complex contagion phenomenon, in the spreadingof social behavior. As these works can eventually help incontrolling viral spread when such propagation is not desired(like in case of drug-abuse tweets), there is a need to lookinto the generation of drug-abuse tweets through the prism ofsuch models. As there is still a wide gap in understanding thecharacteristics of the social network through which such drug-abuse tweets spread and the role of the users that influence spreading of drug-abuse content, we believe this paper wouldcontribute in filling this gap. In the next section, we describe
TABLE I: List of generic and brand names of prescriptionopioids medically used to treat pain . Generic names Brand names oxycodone OxyContin, Percodan, Percocethydrocodone Vicodin, Lortab, Lorcetdiphenoxylate Lomotilmorphine Kadian, Avinza, MS Contincodeine -fentanyl Duragesicpropoxyphene Darvonhydromorphone Dilaudidmeperidine Demerolmethadone - the dataset used for this study.III. D
ATASET
In this section, we provide a detailed description of theTwitter dataset along with the data collection methodology andthe preprocessing techniques used. We subsequently describethe classification technique used to identify tweets that arepromoting or reporting prescription drug-abuse. In line withthe literature [5], the corresponding users engaged in suchtweets are henceforth termed as drug-abusers . Based on thefollower relation among these drug-abusers, a network iscreated. The steps followed to form the network is pictoriallyrepresented in figure 1.
A. Data Collection
The data collection steps can be briefly described as follows:1) We prepared a set of drugs names (see table I) that havebeen marked and listed for abusive use in the past by theNational Institute on Drug Abuse (NIDA) . The genericand brand names of these drugs were used as search keywords for collecting the drug-related tweets using theweb-based crawler, “ Get Old Tweets ”. This provided allthe searchable tweets from January 2012 to July 2017containing the drug names.2) As only limited information about the tweets was beingprovided by the web-based crawler, we used the “ tweetid ” of the returned tweets to further query and extractthe complete meta-data using the Twitter API .3) As retweets could not be retrieved using this web-basedcrawler, they were obtained using a different TwitterAPI .4) Finally, non-English tweets were identified usingLangID and discarded.Using this approach, we collected more than million drug-related tweets. However, we observed that this collected tweetset included both kinds of tweets: those promoting drugs orreporting drug-abuse as well as those spreading awarenessor rehabilitation and treatment information, that we term asnon-abuse tweets. Hence, we applied several machine learningtechniques to identify drug-abuse tweets, which is detailed inthe next section. https://teens.drugabuse.gov/drug-facts/prescription-pain-medications-opioids https://api.twitter.com/1.1/statuses/show.json https://api.twitter.com/1.1/statuses/retweets/:id.json https://github.com/saffsd/langid.py B. Classification of Drug-Abuse Tweets
TABLE II: Performance of binary classification of prescriptiondrug-abuse tweets. 10-fold cross-validation is used to measurethe F score of the two classes (Drug-Abuse and No-Abuse)and the overall accuracy of the classifier. Classifier DA F NA F Accuracy
N-grams as features and handcrafted featuresNaive Bayes .
752 0 .
701 72 . SVM .
787 0 .
759 77 . Random Forest .
842 0 .
794 82 . Logistic Regression .
701 0 .
694 69 . AdaBoost .
740 0 .
613 68 . XGBoost .
776 0 .
694 74 . Bagging .
770 0 .
752 76 . Voting .
786 0 .
758 77 . Sentence embeddings and handcrafted featuresNaive Bayes .
758 0 .
735 74 . SVM .
857 0 .
846 85 . Random Forest .
814 0 .
806 81 . Logistic Regression .
811 0 .
803 80 . AdaBoost .
782 0 .
770 77 . XGBoost .
817 0 .
810 81 . Bagging .
795 0 .
780 78 . Voting .
843 0 .
832 83 . Deep learning with word embeddingsLSTM .
807 0 .
812 81 . RNN .
819 0 .
820 81 . RCNN [39] .
805 0 .
812 80 . TextCNN [40] .
830 0 .
837 83 . One of the important requirements in identifying the drug-abusers is to classify the tweets based on whether they promote(or self-report) prescription drug-abuse or not. As a signif-icant proportion of the tweets are meant towards increasingawareness against drug-abuse, we need to filter out tweetsthat promote or self-report drug-abuse from the rest of thetweets. Taking a cue from the works related to the automaticidentification of prescription drug-abuse tweets [16], [17],[41], [42], we investigated several supervised classificationbased approaches to filter out drug-abuse tweets from the setof tweets collected using keyword search. We proceeded withtext classification as follows:
Data Annotation: :
We manually annotated , tweets,containing different themes (see table III) that whereidentified through an exhaustive manual investigation madeby annotators on , tweets from the collected dataset.These , were selected randomly from the collected data.We subsequently, selected unique tweets, randomly, fromeach theme for annotation to create a balanced annotatedtraining set of , tweets. Each tweet was subsequentlylabeled as ’Drug-Abuse (DA)’ or ’Non-Abuse (NA)’ by annotators and inter-annotator disagreements were solved bymajority voting. The themes from table III can be groupedinto DA or NA categories with each group having 7 themes.Hence the resulting dataset used for measuring classificationperformance is balanced and has equal number of drug-abuseand non-abuse tweets (i.e. , tweets per category). Feature Selection: :
We use three different feature sets forbinary classification, based on the classifier, as follows:1) A combination of bi-gram vector and handcrafted fea-tures, proposed in [16].
Tweetsmatching keywords
Fig. 1: Steps of follower network formation.TABLE III: Example of the variety of tweets that match our keywords. The keywords (listed in table I) that are used to searchprescription drug-abuse tweets are highlighted. All the tweets in this table are paraphrased to maintain the anonymity of theusers.
Drug-Abuse Examples Non-Abuse ExamplesCategory Tweet Category TweetAddiction
I was an addict, a complete addict! I was consuming morethan < NUMBER > mg of Morphine and
OxyContin eachday.
Metaphor / Sarcasm /Jokes
What you call Alabama Shakes we call that
OxyContin withdrawal in the state of Ohio.I am officially addicted to
Vicodin ... I need help. My grandmother was telling about how much she moneycould earn by selling her
Percocet on the streets. lmfao.
Co-ingestion
Washing
Demerol down my throat with some vodka. Isense that I have officially failed at life.
Awareness
Left over
Vicodin : Flush or Trash? Link to FDA for SafeMedication Disposal. < URL > . A useful homepage linkfor patients? Vicodin with Weed = a long sleep. The CDC says < NUMBER > people died this year fromprescription opioid overdose. PercocetAlternate modes of in-gestion
I’m sitting on a large leather chair railing a ton of
Dilaudid . Rehabilitation Vicodin
Rehab in Florida, Florida Center for Recovery < URL > .I’m about to snort some of the OxyContin off my table
OxyContin and Transition toHeroin @ Trusted Heroin Rehab < URL > Recreation
Have I at any point referenced how much I recreationallyenjoy
Vicodin ? Pop-culturereferences OxyContin , Xanax bars,
Percocet and
Lortab / Valiums,Morphine patches, ecstasy / It’s all up for grabsHaving a
Vicodin party at my place, who wants to join?
Vicodin . Can you?
Selling
I’m amassing all my remaining
Vicodin and
Percocet from my previous two medical procedures and sellingthem as soon as I get back to the burgh
News
Washington city devastated by
OxyContin addiction suesPurdue Pharma — claiming drugmaker put profits overcitizens < URL > Giving out
Percocet , $ < NUMBER > a pill... Get yourhands on them while they last!! Heroin makes lethal comeback after OxyContin becomesmore difficult to crush - Alaska Dispatch < URL > Ingestion
One of the metrits is that I get to pop
Vicodin like breathmints. So that’s always a good thing.
Medical treatment
Consumed a
Vicodin to get rid of the pain in my mouthonly to throw out everything a few hours after my surgery.High as a kite after taking that
Vicodin . Surgery went well, and i’m happy that it’s over. Its timeto take some
Vicodin !! Illegal online pharma-cies
Order High quality
OxyContin
Online, < NUMBER > %discount. No Prescription Required < URL > Pain
Sadly, the
Percocet isn’t helping me with my knee pain.I may need to explore something different.Did someone say
Percocet ? Buy
Percocet
Online < URL > My knee is in great pain. I need to take a
Percocet forthe pain.
2) A combination of semantic sentence embedding,Sent2Vec [43], and handcrafted features.3) Word embeddings using GloVe.Compared to the n -gram based feature generation approachproposed in [16] that generates a large set of features (around , ), the feature set generated by Sent2Vec is muchsmaller (around ). The handcrafted features used in lit-erature to classify drug-abuse tweets include the presenceand count of ( a ) specific abuse-indicating keywords that mayindicate frequent overdoses, co-ingestion, alternative motivesand routes of drug admission [5], [44], and ( b ) keywords rep- resenting drug-related slang and colloquial words . Each wordin GloVe embedding was represented using a dimensionvector. Classification: :
We use 10-fold cross-validation to reportclassification results. In each iteration of the 10-fold, tweets inthe training set and test set were sampled randomly, ensuringan equal proportion of drug-abuse and non-abuse tweets inboth the sets. This was done using the “Stratified K-Foldscross-validator” library of scikit learn, which ensured thatthe percentage of samples from each class were preserved in training and testing set during each fold. In each fold, thesampling for the test set and training set was done with ratio, ensuring that the tweets from the test sets of previousiterations are not repeated in the latest test set.We used several machine learning as well as deep neuralnetwork based methods for classification. The machine learn-ing models included Naive Bayes, SVM, Random Forest, Lo-gistic Regression as well as Ensemble learning techniques likeAdaBoost, XGBoost, Bagging and Voting. Decision Stumpwas used as the base classifier for AdaBoost and Bagging,while SVM, Logistic Regression and Naive Bayes classifierswere used as the base classifiers in Voting ensemble wherethe majority of the label predicted by the three classifiers wasconsidered as the label. These models were trained on twodifferent feature sets as, mentioned in (1) and (2). The deeplearning models used include LSTM, RNN, RCNN [39] aswell as TextCNN [40] and were trained on word embeddingsmentioned in (3).While LSTM and RNN are commonly used deep learningtechniques for text classification, RCNN tries to improveupon them by incorporating contextual information in therecurrent structure. In contrast to the recurrent deep learningarchitectures, TextCNN adapts CNN for sentence classifica-tion, making it relatively faster to train and requires littlehyperparameter tuning. All the deep learning models weretrained with GloVe embeddings as inputs, where each wordwas represented by a 100 dimension vector. The LSTM modelwas parameterized with a dropout of and recurrent-dropout of . We used bidirectional GRU as the recurrentlayer in RNN model and its output was max-pooled andaverage-pooled. The concatenation of the max-pooled andaverage-pooled vectors was given as inputs to the dense layerfor classification. The RCNN model was parameterized togenerate dimensional (left and right) context vectors.In the TextCNN model, the kernel-size of the (parallel)convolution layers were , and respectively. Each of itsconvolution layers had 128 filters. The output of the threeconvolution layers were max-pooled, concatenated and givenas input to the dense layer. Table IV gives a summary of theimportant parameters for these DL models.TABLE IV: Description of the model parameters. Parameter Value (Remarks)LSTM
Dropout . Recurrent Dropout . RNN
Recurrent Layer Type = Bidirectional GRU (Outputs ofthis layer were max-pooled andaverage-pooled.)Dense Layer Input = Concatenation ofAverage-pool and Max-Pool layers
RCNN
Left Context dim =
Right Context dim =
TextCNN
Parallel CNN layers 3CNN Layer 1 Kernel size = 2 , Filters = 128CNN Layer 2 Kernel size = 3 , Filters = 128CNN Layer 3 Kernel size = 5 , Filters = 128
Observations: :
Table II compares the -fold cross-validation accuracy (applied on the , annotated tweets)of different Machine Learning (ML) and Deep Learning (DL)classifiers in identifying the abuse and non-abuse tweets.While DL classifiers generally perform better than ML clas-sifiers, we observe that SVM trained with a combination ofsentence embeddings and hand-crafted features outperformedall the classifiers. Based on the classification performance ofSVM, it was used for further classification of 2.2 milliontweets.Although the accuracy of our approach in identifying thedrug-abuse tweets is significantly high, however, we inves-tigated some of the reasons for misclassification. From fig-ure 2(a) it is evident that the correctly classified drug-abuse(DA) tweets prominently contain drug-abuse related slangterms (like oxycotton, hillbilly, percs, etc.) and keywordshinting at co-ingestion (like alcohol, beer, etc.), while correctlyclassified non-abuse (NA) tweets as seen in figure 2(c) haverelatively low slang terms and co-ingestion keywords buthigher mentions of motive keywords (like surgery or stress)and side-effects (like insomnia or migraine). While it isdifficult to determine the exact reason for misclassification, butbased on the evidence it is highly likely that NA tweets mightbe misclassified as DA (figure 2(b)) due to the presence ofslang terms and co-ingestion keywords. On the other hand NAtweets might be misclassified as DA tweets due the relativelyhigher presence of motive terms and keywords hinting at side-effects.Out of the . million tweets, the classifier identified around . million tweets ( of total tweets), of , uniqueusers, as prescription drug-abuse tweets. We subsequentlyused the Botometer [45] API to identify and remove thebot accounts. This service assigns each user a bot scorecorresponding to the likelihood of that account being a bot.The score is calculated based on a set of , features usingaccount metadata, content, network and temporal information.Using a threshold score of 0.5 [45], [46], users werelabeled as bots and their corresponding tweets were discarded.For ethical concerns, we follow a rigid anonymizationmechanism based on guidelines mentioned in [47]. The tweetand user identities were replaced by virtual identifiers. Thecorresponding user mentions in the tweets were also replacedby the corresponding virtual identifier. The timestamps of thetweets were also suitably replaced by relative values. All thetweets provided as examples in this paper were paraphrasedand the URLs were also replaced by placeholders.The observations thus highlight the enormity of the scaleof the drug-abusers active in the social network and thetremendous threat they can pose in spreading of the drug-abuse menace. However, there are a few limitations of thedataset that we outline next. C. Limitations of the Dataset
The dataset considered for this study contains informationabout the users, their followers and the users they followon Twitter, in addition to each user’s prescription drug-abuse https://botometer.iuni.iu.edu/ Naive BayesSVMRandom ForestLogistic RegressionAdaBoostXGBoostBaggingVotingLSTMRNNRCNNTextCNN D r ug S l a ng M o ti v e S i d e − e ff ec t s C o − i ng e s ti on (a) True Positives D r ug S l a ng M o ti v e S i d e − e ff ec t s C o − i ng e s ti on A vg . no r m a li ze d v a l u e (b) False Positives Naive BayesSVMRandom ForestLogistic RegressionAdaBoostXGBoostBaggingVotingLSTMRNNRCNNTextCNN D r ug S l a ng M o ti v e S i d e − e ff ec t s C o − i ng e s ti on (c) True Negatives D r ug S l a ng M o ti v e S i d e − e ff ec t s C o − i ng e s ti on A vg . no r m a li ze d v a l u e (d) False Negatives Fig. 2: Average normalized count of prominent keywords of(a) correctly classified DA tweets, (b) NA tweets classifiedas DA, (c) correctly classified NA tweets and (d) DAtweets classified as NA. ML classifiers trained on sentenceembeddings and DL classifiers trained on word embeddingswere considered.tweets. The web-scraping API retrieves original tweets only,i.e., it does not contain retweets. Hence the Twitter API wasused to collect retweets of drug-abuse tweets. A limitation ofthis API is that it only retrieves 100 most recent retweets ofthe tweet. As a result, we couldn’t retrieve complete retweetinformation of tweets which had more than 100 retweets.Another limitation of this dataset is that it does not containinformation about the time when a user followed someone else.As a result, the network created from this dataset is consideredas a static network and the dynamicity of the edges could notbe considered. D. Qualitative Analysis of the Tweets
We performed a qualitative analysis of the 2.2 milliontweets that were collected in the dataset. Table III providesrepresentative examples of both drug-abuse and non-abusetweets. Majority of the non-abuse tweets, (that contain drug-abuse keywords, but do not promote or report drug-abuse) canbe related to spreading awareness and rehabilitation, news orbe related to reporting effectiveness or side-effects of drugsused during medical treatments. Finally, a small fraction oftweets contained references to pop culture in the form of songlyrics about drug addiction and recovery or prescription drug-abuse references in movies or television shows.As part of the study of the cascades of drug-abuse messages,we initially investigated the underlying follower network of the https://api.twitter.com/1.1/statuses/retweets/:id.json -6 -5 -4 -3 -2 -1 CC D F FollowersFollowing (a) CCDF of followings and fol-lowers. -6 -5 -4 -3 -2 -1 CC D F (b) CCDF of number of tweets ofusers in the network. Fig. 3: (a) represents CCDF of the follower count andfollowing count of the users and (b) represents CCDF ofthe number of tweets of users in the network.drug-abusers along with their engagement characteristics, bothof which are major drivers of these cascades. We next describethe process of creating the follower network and describe someof its characteristics that play major roles in the spread of thecontents. IV. T HE F OLLOWER N ETWORK
As the network provides the underlying framework for thespread of the drug-abuse tweets, we observe some of itsessential properties and highlight their significance. However,we first briefly outline the steps of the formation of thenetwork.
A. Network Formation
We used the user information and their corresponding tweets(or retweets) to create the follower network of these users. Foreach of the , unique users (denoted as U ) identifiedfrom the . million abuse tweets and retweets, we used theTwitter API to identify the follower relation between a userand the remaining unique users. The resulting network is adirected graph represented as G = h V, E i , where V is theset of nodes represented by the users in U and E is the setof directed edges between the node pairs. A directed edge iscreated from node j to i (denoted as e ij ) if user u i is followedby u j .We next observe the properties of the network and investi-gate the possible support it can provide in spreading of drug-abuse tweets. B. Characterizing the network
We highlight some of the significant network properties(summarized in table V) that would impact the spreading ofdrug-abuse tweets. https://api.twitter.com/1.1/followers/list.json https://api.twitter.com/1.1/friends/list.json TABLE V: Statistics of the follower network.
Network Property Value
Number of nodes , Number of links , , Average (in/out) degree . In-degree exponent . Out-degree exponent . Number of connected components
Giant component size , Clustering coefficient . Reciprocity . TABLE VI: Distribution of the users across different Bowtiecomponents.
Component Count Percentage
LSCC ,
027 91 . IN ,
578 7 . OUT ,
467 1 . Tendrils ,
224 0 . Basic Statistics:
We observed that there exists a large net-work consisting of approximately . million unique users,with million links between them. The number of followers(in-degree) and followings (out-degree) of the nodes in thisnetwork follow power-law distributions with exponents . and . , respectively. Figure 3(a), shows the complementarycumulative distribution (CCDF) of the number of followersand followings within the network. The in-degree exponentindicates that a significant fraction of drug-abusers have a veryhigh number of followers ( of users have more than followers and . , i.e. , users, have more than followers in the network), suggesting the possibility of a sig-nificant spread of the drug-abuse tweets if suitable connectionsexist among the nodes across the network. Consequently, weobserved three major structural properties of this network —the connectedness among the nodes, the average clusteringcoefficient and the reciprocity of the links — all of which playan important role in the spread of tweets and can subsequentlyimpact the user engagement. Connectedness:
To observe the connectedness of the net-work, we looked at the number of connected components,i.e., subgraphs where all the nodes within it are connectedthrough a path and have no additional connections to any othernodes outside the supergraph. We observe that although thereare connected components in the network, however thelargest (giant) component comprises of . of the totalnodes (around , nodes), indicating that the networkis almost entirely connected. The second and the third largestconnected components have and nodes respectively, andthere exist several smaller components with an average size ofaround . Further, if we model the (giant component) networkas a BowTie structure [48] it is found that around of thenodes (refer table VI) fall in the largest connected component(LSCC) or the core of the structure with much fewer nodes inthe IN and OUT components. A large core, apart from beingresilient to targeted attacks, also implies the possibility offaster diffusion of drug-abuse tweets over a significant fractionof the network [49]. Clustering Coefficient:
This undirected network exhibitsa high average clustering coefficient of around . that is significantly higher than observed in the actual Twitternetwork ( . ) [50]. Although a high clustering coefficienthas generally been considered as an impediment to large-scalediffusion across the networks [51], however, it needs to beinvestigated how the high clustering coefficient impacts thecascade properties in the drug-abuse networks. Reciprocity:
Our investigation further reveals the existenceof very high reciprocity ( of total links) in the network.This value is significantly higher than the reciprocity value ofaround 22% observed in the Twitter follower network studiedin [52]. Previous studies have indicated that the existenceof high reciprocal links not only affects the coverage of thespread of messages in social networks but also enhances thespeed of the diffusion [53].We later investigate the impact of these structural propertiesof the network on the cascades. However, these statistics pointtowards the existence of an underlying network platform thatis amenable to the spread of the drug-abuse tweets throughactive engagement of a set of users. Hence we next attemptto characterize the users in the network by their engagementpattern.V. C
HARACTERIZING U SERS IN THE N ETWORK
In information diffusion, users playing dominant roles inthe spreading processes have often been identified based onthe importance of their contents, their positional significancein the network and their engagement time. In this section,we focus on the engagement time along with the positionalsignificance to characterize the users and deal with the contentsseparately in the later section. While the engagement time oractiveness of the users can contribute to the speed of diffusion,the positional importance can help in increasing the breadth ordepth of the cascades [54]. We initially provide measures forboth activeness and positional importance and subsequentlycharacterize the users based on both these parameters.
A. Activeness of User
All users are not equally active in tweeting about pre-scription drug-abuse. Figure 3(b) shows the complementarycumulative distribution of the number of tweets of the users.The figure highlights that there exists a significant fraction ofusers with a vast number of tweets, with , users with morethan tweets and users with more than tweets. Weconsider a user as an active user if one tweets more with low latency (a gap between two consecutive tweets). The latencybetween two tweets is calculated based on the creation timeof each tweet made available by the Twitter API. To avoidany confusion, we re-emphasize that Twitter does not providethe time when a user starts following someone. Thus the activeness score of user i , denoted as φ i is defined as follows: φ i = | T i | l i , if | T i | > , otherwise (1)where, T i = { t , t , . . . , t n } is the set of sorted timestampsof the corresponding tweets of user i , | T i | is the total number TABLE VII: Categorizing user of the network based on theiractivity.
Users category Number of users
Highly active users , Moderately active users , Inactive users , of tweets by user i , and l i is average latency between twoconsecutive tweets of user i that can be defined as follows: l i = 1 | T i | − | T i |− X k =1 ( t k +1 − t k ) = 1 | T i | − (cid:0) t | T i | − t (cid:1) (2) -6 -5 -4 -3 -2 -1 -6 -5 -4 -3 -2 -1 CC D F activity score Φ i of user (a) CCDF of user activity score inthe network. -6 -5 -4 -3 -2 -1 -8 -7 (cid:1)(cid:2) -6 (cid:3)(cid:4) -5 (cid:5)(cid:6) -4 C(cid:7)(cid:8)(cid:9) h(cid:10)(cid:11) (cid:12)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:20)(cid:21)(cid:22)(cid:23)(cid:24)(cid:25)(cid:26) (cid:27)(cid:28)(cid:29)(cid:30)(cid:31) !" (b) Hub score and authority scorefor users.
Fig. 4: (a) represents the CCDF of users’ activity score as perequation 1, (b) represents CCDF of the Authority and Hubscore of the users calculated using HITS algorithm.The distribution of activity score as shown in figure 4(a) isa heavy-tailed power-law distribution. To categorize the usersbased on the activity score, we used the Head/Tail breaksalgorithm [55] to cluster the distribution into 2 parts. Userswith φ i > . × − (i.e. the tail) were classified as highlyactive users. The remaining users were further classified into2 categories, moderately active ( < φ i ≤ . × − ) and inactive ( φ i = 0 ). Table VII shows the number of usersbelonging to each category according to activity score. B. Positional Importance
The position of a user in the network can determine herreachability (ability to reach a broad set of users through hertweets) as well as her accessibility (ability to receive tweetsfrom a large number of users). To capture both these charac-teristics simultaneously, we calculated the hub and authorityscore of each user in the network. Authority score of a node ishigh if it is followed by nodes with high hub score, whereasthe hub score of a node would be high if it follows nodeswith high authority scores. Thus, while authorities can act asgood information spreaders because of their followers, hubscan act as information collectors obtaining diverse informationfrom different authorities. We use the HITS algorithm [56] tocalculate authority and hub score of each user.Figure 4(b) shows the CCDF of the hub and authorityscores. We labeled the users as high authority user if itsauthority score is above × − (obtained using Head/tail breaks algorithm [55]) and the rest of the users are labeledas low authority users. Those users having hub score above × − using the same algorithm are labeled as high hubuser, and the rest of the users are labeled as low hub users.We categorized the users into four role types based onauthority and hub scores: a) information seeking – who havehigh hub and low authority scores, b) information sharing –who have high authority and low hub scores, c) leaders – whohave high hub as well as high authority scores and d) fringe – who have low hub and low authority scores.In table IX, we observed that around of the total usersare fringe nodes who have few followers as well as very fewfollowings. On the other hand, the total number of users ineach of the remaining three categories is only − . Theusers in the three remaining categories represent the influentialsection of users in the network who have the capability tospread drug-abuse tweets across a large section of the network.Thus it is necessary to investigate the contribution made byeach of these user types in the spread of drug-abuse tweets;hence we next correlate the activity score of the users withtheir hub and authority scores to explore their potential inspreading drug-abuse tweets. C. Characterizing Highly Active Users
Initially, we took a closer look at the active users andobserved their role types. The first row in table VIII shows thenumber of active users in each of the role categories. As can beobserved, more than of the highly active users are fringenodes. This indicates that even though fringe nodes hold lesspositional importance but a significant fraction of the activeengagements in generating drug-abuse contents is made bythem. Thus to investigate the fraction of users getting exposedto the drug-abuse tweets generated by these active users, wefurther observed the reach of the active nodes at different hops.As shown in table VIII, the active nodes by themselves canreach only of the network in the first-hop but manageto reach of the network in the second-hop. Thus, thereachability of the first-hop neighbors provides the active usersthe potential to reach the bulk of the nodes in the network.On taking a look at the properties of the first-hop neighbors,we find that around of these nodes have either a highhub or authority score i.e. they are non-fringe users, includingmore than leaders who have both high hub and authorityscores. Roughly . million or of the users in thesecond-hop follow at least one non-fringe user in the first-hop, highlighting the importance of the connectivity of non-fringe nodes. Interestingly, we also observed that of thefirst-hop neighbors follow one or more active fringe nodes,indicating that even though individually the active fringe nodesare not structurally important but collectively they can reacha significant number of users in the first-hop.Thus a major takeaway from these observations is thatalthough most of the active users are positionally fringe,however, due to the positional importance of their first-hopneighbors, drug-abuse discussions initiated by these nodescan potentially reach a significant population of users in thenetwork. We next observe the actual cascades and investigate TABLE VIII: Reach of highly active users at each hop. Hop shows the distribution of highly active users by their role inthe network followed by the distribution of users roles at each subsequent hop. Hops Info.Sharing Leaders Info. Seeking Fringe ,
297 4 ,
436 1 . ,
828 2 ,
741 79 ,
985 96 ,
364 22 . ,
251 2 ,
191 272 ,
548 374 ,
761 89 . ,
155 411 ,
928 98 . ,
256 414 ,
184 98 . ,
314 98 . TABLE IX: Properties of different user roles.
User Role
Fringe ,
348 24 .
97 27 . Info. seeking ,
979 72 .
48 133 . Leaders ,
167 467 .
51 466 . Info. sharing
823 1877 .
20 110 . the role of the underlying network along with the key playersand the tweet contents in the spreading process.VI. C ASCADES AND S PREAD
To measure the extent of the spread and influence oftweets, we investigate the cascades formed through drug-abusediscussions. We discovered the key players along with thepattern of user engagement responsible for the formation ofthe cascades. Here user engagement refers to both generationof new drug-abuse tweets as well as re-tweets by the users.Subsequently, the dynamics of spread with respect to thedrug names are investigated, keeping in mind the complexcontagion phenomenon that is typical to the spread of socialbehavior.
A. Measuring Cascades
We initially describe the experimental procedure to identifythe cascades followed by the measures of various propertiesof the cascades.
Dataset Preparation:
The cascades might be formed whenusers directly retweet a drug-abuse tweet or create a freshcontent based on one that has appeared in their timeline.While retweets can directly be linked to a cascade, determiningwhether a new drug-abuse tweet has been made based onthe previously received tweet (and hence should be a part ofthe cascade) is difficult. Possibilities exist that the user mighthave been influenced by certain external sources and not thedrug-abuse tweet she has received before tweeting. However,ignoring such tweets entirely as not being part of the cascadescan lead to a severe undermining of the veracity of the cascadeproblem. Hence to reduce the chances of such coincidentalerrors , following assertions were made: a) a tweet T wasadded to the cascade if at least one previous tweet from thecascade appeared on the user’s timeline within a short period, ∆ , prior to the sending of T and b) we consider only largecascades for analysis so as to ensure that a significant fractionof the spread does not suffer from such error. The value of ∆ was chosen as nine days based on the study in [57], whereit is shown that the mean of the attention decay time (timebetween peak attention and of attention) of the tweets -5 -4 -3 -2 -1 CC D F (a) CCDF of cascade size. ABDEF GHIJK LMNOP QRSTUVWXYZ[\]^_‘bcdefgijklmnopqrstuvwxyz{|}~(cid:127)(cid:128)(cid:129)(cid:130)(cid:131)(cid:132)(cid:133)(cid:134)(cid:135)(cid:136)(cid:137)(cid:138)(cid:139)(cid:140)(cid:141)(cid:142)(cid:143)(cid:144)(cid:145)(cid:146)(cid:147)(cid:148)(cid:149)(cid:150)(cid:151)(cid:152)(cid:153)(cid:154)(cid:155)(cid:156)(cid:157)(cid:158)(cid:159)(cid:160)¡¢£⁄¥ƒ§¤'“«‹›fifl(cid:176)–† ‡·(cid:181)¶•‚„ ”»…‰ (b) Structural Virality.
Fig. 5: (a) represents CCDF of the cascade size (a) representsthe relation between cascade size and mean structural virality(Wiener index) for each bin.is around hours. The process of identifying cascades isformally defined below.The drug-abuse tweets in the dataset are initially sortedbased on their time of generation. For each tweet, the cor-responding creator is identified and is included as the initialnode in the cascade graph G = h V, E i . A user, v , followingthe initiator i is added as a node to the cascade graph ifit has either re-tweeted or created a new drug-abuse tweetwithin nine days of the appearance of the parent tweet in hertimeline. A directed link is created from node i to the follower v , indicating that engagement of node v has possibly beeninfluenced by i . This process is further recursively repeatedfor the followers of the newly added users in G . By followingthis process, we extracted around , cascades of differentlengths. We focus on the large cascades as they mainly reflectthe threat posed by social media in the spread of drug-abusetweets. To study the characteristics of the large cascades, weconsidered cascades of length ≥ for our investigations. Thechoice of this value is not a principled one but is based onour observation that users with different characteristics play aconsistent role across cascades beyond the length of . Wenext investigate the key structural properties of these largecascades. Structural Properties of the Cascades:
The distribution ofthe cascade sizes provides an idea about the scale of userengagement. As shown in figure 5(a), the distribution ofthe cascade sizes follows a power-law with an exponent of . . The maximum cascade size observed is , , whichindicates large cascades of user engagement may be formeddue to the spread of drug-abuse tweets.We also observed the structural virality of these cascades,as defined in [58]. The structural virality has been measuredusing the Wiener index that is given by the average shortestpath length ( d avg ) between any pair of nodes in the cascade ( , ]( , ]( , ]( , ]( , ]( , ]( , ] L e n g t h Cascade subgraph size avg. shortest path lengthavg. diameter (a) Avg. Path Length and Diameter. ( , ]( , ]( , ]( , ]( , ]( , ]( , ] (cid:190)¿(cid:192)`´ Cascade subgraph size agv. clustering coefficientavg. reciprocity (b) Avg. Clustering Coeff. andReciprocity.
Fig. 6: Properties of cascade nodes in network subgraph. (a)shows the average shortest path and diameter of the cascadenodes in network subgraph and, (b) shows the averagereciprocity and clustering coefficient.graph. A lower value of d avg (near to ) indicates a hub-like structure where a single powerful node causes the entirecascade, whereas larger values indicate viral diffusion throughbranches involving multiple propagating nodes. Figure 5(b)shows the distribution of the structural virality observed in thefollower network. As can be observed, the structural viralitysteadily increases with increasing cascade size. This indicatesthat multiple nodes play an important role in the cascades.
1) Subgraph Properties of the Cascade Nodes:
To study thenetwork structure of the nodes involved in the large cascades,for each cascade we constructed a network subgraph thatcomprises of the nodes of the corresponding cascade. Asshown in figure 6(a), the average path length between thenodes in the subgraph vary from . to . , whereas thecorresponding average diameter ranges from . to . with respect to the subgraph sizes. These values indicatethat these cascades reach far beyond the immediate neighbornodes. It is also observed that the mean reciprocity andclustering coefficient of these subgraphs are significantly high(figure 6(b)). The mean reciprocity values with respect to thesubgraph sizes vary between . and . , whereas the meanclustering coefficients range between . and . . A highaverage clustering coefficient and reciprocity of the cascadenodes provide strong evidence that the cascades spread alongthe follower chain through groups of closely connected nodes.We next focus on the users to identify the key playersinvolved in the spread of the drug-abuse tweets. B. Key Players in Spreading
We investigated the key players in the cascades consideringboth the activeness as well as the positional importance ofthe users. Since a large fraction of the users in the networkis largely inactive, we initially observed the activeness of theusers in the cascade. We observed that for cascades involvingmore than users, around − of the users are onetime engagers who had contributed only one drug-abuse tweetbut helped in keeping the cascade alive. This reveals theimportance of these inactive users who contribute to increasingthe length of the cascades. -5 -4 -3 -2 -1 ˆ˜ ¯˘ ˙¨(cid:201)˚ ¸(cid:204)˝˛ ˇ—(cid:209)(cid:210) (cid:211)(cid:212)(cid:213)(cid:214) (cid:215)(cid:216)(cid:217)(cid:218) (cid:219)(cid:220)(cid:221)(cid:222) (cid:223)(cid:224) CC D F activity score Æ(cid:226)ª(cid:228) (cid:229)(cid:230)(cid:231) ŁØŒº(cid:236)(cid:237)(cid:238)(cid:239)(cid:240) æ(cid:242)(cid:243)(cid:244)ı(cid:246)(cid:247)łø œß(cid:252)(cid:253)(cid:254)(cid:255)1-(cid:0)(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18) (cid:19)(cid:20) (cid:21)(cid:22)(cid:23) (cid:24)(cid:25) (cid:26)(cid:27) (cid:28)(cid:29) CC D F (a) CCDF of node properties. Info. sharing
L()*+,.
Info. seeking
N/02
Fringe Fringe
P456789:;<= D>?@ABCEFGHI JK MOQRS in each user role
TUVWXYZ[\]^ _‘ abcdefghij klmno pqrs tuvw user role (b) User distribution in the net-work.
Fig. 7: (a) represents CCDF of activity score and the insetin (a) represents CCDF of the of the drug-abuse tweets (asseen in figure 7(b)) in the timeline of a random user aregenerated by a non-fringe node, even though they constituteonly of the nodes in the network. A closer look at table IXreveals that in-degree of non-fringe nodes are times higher(computed using weighted average) compared to in-degree offringe nodes. So the probability that a node follows a non-fringe node is comparable with the probability that the nodefollows a fringe node. Hence, as the fraction of fringe and non-fringe nodes followed by a random user is comparable, thecontents generated by both these node types in the timeline ofa random user is also comparable. This indicates that both thenon-fringe as well as the fringe nodes are similarly responsiblein the spread of these drug-abuse tweets. C. Role of Neighbors in Spreading
We next focus our attention on the influence of neighborsin the spreading of user engagement. For this experiment,cascades of size > were considered. Table X comparesthe properties of these cascades initiated by fringe nodesand non-fringe nodes. It is evident that cascades initiated bynon-fringe nodes have a greater size on average with morenodes (aggregates for all cascades) in its first and second-hop.Irrespective of the type of the initiator, the presence of non-fringe nodes in the first-hop play an important role in inductingnodes in the second-hop of the cascades. This phenomenon isevident from cascades initiated by fringe nodes where only of first-hop nodes belong to the non-fringe category but bringin of the nodes in the second-hop. It is also observed thatthe maximum width of the cascades initiated by fringe nodesoccurs at more depth as compared to the ones generated bytheir counterparts. This further indicates that these cascades TABLE X: Comparison of the properties of cascades initiated by fringe and non-fringe nodes. The category of users involvedplay an important role in determining the properties of the cascade they belong to.
Cascade Property Cascades initiated by fringe nodes Cascades initiated by non-fringe nodes
Value σ Percent Value σ Percent - .
72% 192 - . Avg. cascade size .
78 1237 . - .
67 458 . -Avg. structural virality ( d ) .
63 3 . - .
97 1 . -Max depth of cascade - - - -Avg. depth of cascades .
72 22 . - .
83 8 . -Avg. depth at which max. widthwas observed in cascade .
95 14 . - .
02 4 . -Avg. .
05 8 . - .
05 37 . -Avg. .
27 0 .
53 5 .
36% 1 .
44 1 .
59 5 . Avg. .
77 8 .
79 94 .
64% 26 .
60 37 .
11 94 . Avg. .
14 22 . - .
87 11 . -Avg. .
64 22 .
03 44 .
77% 3 .
39 9 .
25 43 . Avg. .
49 7 .
52 55 .
23% 4 .
48 6 .
70 56 . xyz{ |}~(cid:127)(cid:128)(cid:129)(cid:130)(cid:131) (cid:132)(cid:133)(cid:134)(cid:135) (cid:136) (a) Overall (cid:137)(cid:138)(cid:139)(cid:140) (cid:141)(cid:142)(cid:143)(cid:144)(cid:145)(cid:146)(cid:147)(cid:148) (cid:149)(cid:150)(cid:151)(cid:152) (cid:153) (cid:154)(cid:155)(cid:156)(cid:157)(cid:158)(cid:159)(cid:160)¡
0 2 4 ¢ £ ⁄¥ƒ§ ¤'“«‹›fifl (cid:176)–†‡ · (b) Vicodin (cid:181)¶•‚ Exposure size k p ( k ) Exposure size k (c) Percocet p ( k ) Exposure size k „”»… p ( k ) Exposure size k (d) OxyContin p ( k ) Exposure size k (e) Lortab
Fig. 8: Average exposure curve for drug names. p ( k ) is the fraction of the network users who tweet about a particular drug-name directly after their k th exposure to it, given that they had not tweeted about it previously. The inset in figures (b), (c)and (d) shows the behavior of structural virality near the peaks at k = 1 . ‰(cid:190)¿(cid:192)` ´ˆ˜¯˘˙¨ (cid:201)˚¸(cid:204)˝˛ˇ P e r c o c e t —(cid:209)(cid:210)(cid:211)(cid:212)(cid:213)(cid:214)(cid:215)(cid:216) (cid:217)(cid:218)(cid:219)(cid:220)(cid:221)(cid:222)(cid:223)(cid:224)Æ(cid:226)ª(cid:228)(cid:229)(cid:230)(cid:231)Ł (a) Stickiness ØŒº(cid:236)(cid:237)(cid:238)(cid:239) (cid:240)æ(cid:242)(cid:243)(cid:244)ı(cid:246) P e r c o c e t (cid:247)łøœß(cid:252)(cid:253)(cid:254)(cid:255) L(cid:0)(cid:1)(cid:2)(cid:3)(cid:4) P e r s i s t e n c e (b) Persistence Fig. 9: Stickiness and persistence score measures for drugnames as defined in [7].survive a few initial hops with the help of other fringe nodesonly to peak later with the help of certain non-fringe ones,thus revealing an organic collaboration of the non-fringe aswell as fringe nodes in the spreading process.Thus we discover that all category of users, fringe and non-fringe as well as active and non-active, contribute significantlyto generating the cascades, highlighting a sizeable collectivephenomenon. We next investigate the engagement behavior ofusers based on the contents (drug names) to discover whetherTwitter serves as a more effective spreading media for certaintypes of drugs.
D. Stickiness and Persistence
Information diffusion concerning different content typeshas been studied using measures like stickiness and persis-tence [7], [38]. We use these measures to investigate theengagement behavior of the users with respect to the drugnames. We investigate how repeated exposure to drug-abusetweets with specific drug names influences the probability ofadopting a similar engagement behavior. A user is consideredto be k -exposed if there are k users, whom the current userfollows, who have tweeted about drug-abuse. We use anordinal time estimate measure for deriving the exposure curve p ( k ) , whereby, we calculate the number of users ( I ( k ) ) whogenerate their first drug-abuse tweet (an indication of adoption)after being k -exposed but before being ( k + 1) -exposed. Thisvalue is subsequently compared with the total number of k -exposed users ( E ( k ) ). The exposure curve is represented as p ( k ) = I ( k ) E ( k ) . The stickiness is measured by the maximumvalue of p ( k ) for all observed values of k and the persistence F ( p ) is represented by the ratio of the area under the exposurecurve and the minimum area of the rectangle covering theexposure curve entirely. F ( p ) provides a measure of the rate ofdecay in the adoption probability with an increasing number ofexposures after it has reached the peak. A value of F ( p ) near to indicates that repeated exposure to drug-abuse tweets wouldbe required before the user herself starts engaging, indicatingthe presence of a complex contagion phenomenon. Observations:
We obtained the value of p ( k ) for eachdrug type present in our dataset. Figure 8 shows the average exposure curves for all the data and four major drug-names(determined based on . and . , respectively) com-pared to the other drugs. In both the cases, peaks are found at k = 1 , indicating that users mostly engage themselves aboutthese tweets after a single exposure only. A similar trend wasobserved for OxyContin, with a peak at k = 0 . This high valueof stickiness is observed for these abused drugs due to theirhigh popularity on Twitter. In contrast, Lortab has a relativelyhigher persistence of . as seen in figure 9(b), hinting thatrepeated exposures continue to have marginal effects on userengagement.To explain the exceptionally high stickiness values forVicodin (figure 8(b)) and Percocet (figure 8(c)) at k = 1 ,we looked into the tweets containing these drug names. Weobserved that a significantly large number of tweets mention-ing Vicodin and Percocet are related to the sale of these drugs(around , and , respectively). Since these tweetsare generated independently, without being exposed, we seehigh values of p ( k ) at k = 0 and for Vicodin and Percocet.Further, since these drugs are popular among the drug-abusers,repeated exposures to tweets related to these drugs do not leadto any significant effect on user engagement, thus lowering thepersistence. Users who are willing to discuss about these drugsrapidly engage themselves after one or two exposures. On theother hand, engagement for drugs, that are less popular overTwitter, shows high persistence. This could be possibly due tothe fact that these drugs being less popular on Twitter, withincreasing exposures the interest of the users about these drugsincreases and hence the probability of engagement remainshigh with the number of exposures.VII. C ONCLUSION
This paper provides a detailed analysis of the Twitterfollower network involving around . million users that areinvolved in the promotion of prescription drug-abuse using theTwitter platform and generating more than 50,000 cascades.We believe that this is a first major work involving such a largescale of data that details the spreading of drug-abuse messagesover Twitter. Analyzing the follower network of drug-abusersreveals a heavy core structure with high local connectivityamong themselves, thereby providing various alternate channelof communication among the users. Investigations on the cas-cades of drug-abuse tweets helped us to discover certain majorfindings. It was discovered that the drug-abuse tweets spreadover long paths across the Twitter follower network throughgroups of closely connected users in the network. It wasalso observed that a significant percentage of cascades beinginitiated and driven by users with low positional importance(with low count of followers as well as its followings), thatwe term as fringe nodes in the network. The spread overthose cascades has been observed to be a result of a collectivephenomenon involving both the important as well as the fringenodes, indicating a resilience to targeted elimination of fewnodes. A diffusion model capturing these dynamics would be helpful in predicting drug related cascades. Consideringthe limited scope of this paper, we would like to developsuch models as a possible extension of the current work.Finally, observations suggest that drug-abusers on Twitterhave much higher risk of adopting newer drugs as increasingexposure of them enhances the probability of adoption. Thesefindings necessitates a deeper and more detailed study of theabuse patterns and user behavior to control the spread of thismenace. R EFERENCES[1] D. S. Fink, J. P. Schleimer, A. Sarvet, K. K. Grover, C. Delcher,A. Castillo-Carniglia, J. H. Kim, A. E. Rivera-Aguirre, S. G. Henry,S. S. Martins et al. , “Association between prescription drug monitoringprograms and nonfatal and fatal drug overdoses: A systematic review.”
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