Julian Sienkiewicz

Statistical analysis of 22 public transport networks in Poland

Public transport systems in 22 Polish cities have been analyzed. The sizes of these networks range from N = 152 to 2881. Depending on the assumed definition of network topology, the degree distribution can follow a power law or can be described by an exponential function. Distributions of path lengths in all considered networks are given by asymmetric, unimodal functions. Clustering, assortativity, and betweenness are studied. All considered networks exhibit small-world behavior and are hierarchically organized. A transition between dissortative small networks N approximately < or = 500 and assortative large networks N approximately > or = 500 is observed.

Negative emotions boost user activity at BBC forum

We present an empirical study of user activity in online BBC discussion forums, measured by the number of posts written by individual debaters and the average sentiment of these posts. Nearly 2.5 million posts from over 18 thousand users were investigated. Scale-free distributions were observed for activity in individual discussion threads as well as for overall activity. The number of unique users in a thread normalized by the thread length decays with thread length, suggesting that thread life is sustained by mutual discussions rather than by independent comments. Automatic sentiment analysis shows that most posts contain negative emotions and the most active users in individual threads express predominantly negative sentiments. It follows that the average emotion of longer threads is more negative and that threads can be sustained by negative comments. An agent-based computer simulation model has been used to reproduce several essential characteristics of the analyzed system. The model stresses the role of discussions between users, especially emotionally laden quarrels between supporters of opposite opinions, and represents many observed statistics of the forum.

Higher order clustering coefficients in Barabási–Albert networks

Higher order clustering coefficients C(x) are introduced for random networks. The coefficients express probabilities that the shortest distance between any two nearest neighbours of a certain vertex i equals x, when one neglects all paths crossing the node i. Using C(x) we found that in the Barabasi–Albert (BA) model the average shortest path length in a nodes neighbourhood is smaller than the equivalent quantity of the whole network and the remainder depends only on the network parameter m. Our results show that small values of the standard clustering coefficient in large BA networks are due to random character of the nearest neighbourhood of vertices in such networks.

Universal scaling of distances in complex networks

Universal scaling of distances between vertices of Erdos-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k(i) and k(j) equals to (l(ij)) = A - B log(k(i)k(j)). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree (k)nn calculated for the nearest neighbors and on network clustering coefficients.

Networks of companies and branches in Poland

In the present study we consider relations between companies in Poland taking into account common branches they belong to. It is clear that companies belonging to the same branch compete for similar customers, so the market induces correlations between them. On the other hand two branches can be related by companies acting in both of them. To remove weak, accidental links we shall use a concept of threshold filtering for weighted networks where a link weight corresponds to a number of existing connections (common companies or branches) between a pair of nodes.

ENTROPY-GROWTH-BASED MODEL OF EMOTIONALLY CHARGED ONLINE DIALOGUES

We analyze emotionally annotated massive data from Internet relay chat (IRC) as well as from BBC forum website and model the dialogues between chat participants by assuming that the driving force for the discussion is the entropy growth of emotional probability distribution. This process is claimed to be responsible for a power-law distribution of the discussion lengths observed in the dialogues. We perform numerical simulations based on the noticed phenomenon obtaining a good agreement with the real data. Finally, we propose a method to artificially prolong the duration of the discussion that relies on the entropy of emotional probability distribution.

Collective Emotions Online

This chapter analyzes patterns in messages posted to several Internet discussion forums from the perspective of the sentiment expressed in them and the collective character of observed emotions. A large set of records describing comments expressed in diverse cyber communities—blogs, forums, IRC channels, and the Digg community—was collected, and sentiment classifiers were used to estimate the emotional valence (positive, negative, or neutral) of each message. A comparison with simple models showed that the data included clusters of comments with the same emotional valence that were much longer than similar clusters created by a random process. This shows that there are emotional interactions between participants so that future posts tend to have the same valence as previous posts. Threads starting from a larger number of negative comments also last longer so negative emotions can be treated as a kind of discussion fuel; when the fuel (negativity) is used up in the discussion, it may finish. Moreover, the amount of user activity in a particular thread correlates positively with the presence of negative emotions expressed by the individual user in the thread. In summary, the analyses describe individual and collective patterns of emotional activities of Web forum users and suggest that negativity is needed to fuel important discussions.

Impact of lexical and sentiment factors on the popularity of scientific papers

We investigate how textual properties of scientific papers relate to the number of citations they receive. Our main finding is that correlations are nonlinear and affect differently the most cited and typical papers. For instance, we find that, in most journals, short titles correlate positively with citations only for the most cited papers, whereas for typical papers, the correlation is usually negative. Our analysis of six different factors, calculated both at the title and abstract level of 4.3 million papers in over 1500 journals, reveals the number of authors, and the length and complexity of the abstract, as having the strongest (positive) influence on the number of citations.

External bias in the model of isolation of communities

We extend a model of community isolation in the d-dimensional lattice to a case with an imposed imbalance between the birth rates of competing communities. We provide analytical and numerical evidences that in the asymmetric two-species model there exists a well-defined value of the asymmetry parameter when the emergence of the isolated (blocked) subgroups is the fastest, i.e., the characteristic time t(c) is minimal. The critical value of the parameter depends only on the lattice dimensionality and is independent of the system size. A similar phenomenon is observed in the multispecies case with a geometric distribution of the birth rates. We also show that blocked subgroups in the multispecies case are absent or very rare when either there is a strictly dominant species that outnumbers the others or there is a large diversity of species. The number of blocked species of different kinds decreases with the dimension of the multispecies system.

Detection and Modeling of Collective Emotions in Online Data

Basing upon emotionally annotated data from four different media (a set of blogs, BBC Forums, Digg portal and IRC channels) we demonstrate the collective character of affective phenomena in online communities. To test whether the emotions of a community member may influence the emotions of others, posts were grouped into clusters of messages with similar emotional valences. The frequency of long clusters was much higher than it would be if emotions occurred at random. Distributions for cluster lengths can be explained by preferential processes because conditional probabilities for consecutive messages grow as a power law with cluster length. Values of characteristic exponent describing this growth correspond to strength of affective attraction for various types of emotions. It is interesting that minor emotions display larger clustering effects, i.e. they interact stronger in a given community. We demonstrate also that our model of emotional clustering leads to emergence of persistent mono-emotional threads when the emotional cluster reaches a critical size. Such ordered patterns have been found in the Blog06 dataset although their number is limited by fluctuations and sentiment classification errors.