Carter T. Butts

Revisiting the Foundations of Network Analysis

Network analysis has emerged as a powerful way of studying phenomena as diverse as interpersonal interaction, connections among neurons, and the structure of the Internet. Appropriate use of network analysis depends, however, on choosing the right network representation for the problem at hand.

4. A Relational Event Framework for Social Action

Social behavior over short time scales is frequently understood in terms of actions, which can be thought of as discrete events in which one individual emits a behavior directed at one or more other entities in his or her environment (possibly including himself or herself). Here, we introduce a highly flexible framework for modeling actions within social settings, which permits likelihood-based inference for behavioral mechanisms with complex dependence. Examples are given for the parameterization of base activity levels, recency, persistence, preferential attachment, transitive/cyclic interaction, and participation shifts within the relational event framework. Parameter estimation is discussed both for data in which an exact history of events is available, and for data in which only event sequences are known. The utility of the framework is illustrated via an application to dynamic modeling of responder radio communications during the early hours of the World Trade Center disaster.

Network inference, error, and informant (in)accuracy: a Bayesian approach

Abstract Much, if not most, social network data is derived from informant reports; past research, however, has indicated that such reports are in fact highly inaccurate representations of social interaction. In this paper, a family of hierarchical Bayesian models is developed which allows for the simultaneous inference of informant accuracy and social structure in the presence of measurement error and missing data. Posterior simulation for these models using Markov Chain Monte Carlo methods is outlined. Robustness of the models to structurally correlated error rates, implications of the Bayesian modeling framework for improved data collection strategies, and the validity of the criterion graph are also discussed.

The interaction of size and density with graph-level indices

Abstract The size and density of graphs interact powerfully and subtly with other graph-level indices (GLIs), thereby complicating their interpretation. Here we examine these interactions by plotting changes in the distributions of several popular graph measures across graphs of varying sizes and densities. We provide a generalized framework for hypothesis testing as a means of controlling for size and density effects, and apply this method to several well-known sets of social network data; implications of our findings for methodology and substantive theory are discussed.

Communication and Cooperation

Communication plays a vital role in the organization and operation of biological, computational, economic, and social systems. Agents often base their behavior on the signals they receive from others and also recognize the importance of the signals they send. Here we develop a framework for analyzing the emergence of communication in an adaptive system. The framework enables the study of a system composed of agents who evolve the ability to strategically send and receive communication. While the modeling framework is quite general, we focus here on a specific application, namely the analysis of cooperation in a single-shot Prisoners Dilemma. We find that, contrary to initial expectations, communication allows the emergence of cooperation in such a system. Moreover, we find a systematic relationship between the processing and language complexity inherent in the communication system and the observed behavior. The approach developed here should open up a variety of phenomena to the systematic exploration of endogenous communication.

Multigraph Sampling of Online Social Networks

State-of-the-art techniques for probability sampling of users of online social networks (OSNs) are based on random walks on a single social relation (typically friendship). While powerful, these methods rely on the social graph being fully connected. Furthermore, the mixing time of the sampling process strongly depends on the characteristics of this graph. In this paper, we observe that there often exist other relations between OSN users, such as membership in the same group or participation in the same event. We propose to exploit the graphs these relations induce, by performing a random walk on their union multigraph. We design a computationally efficient way to perform multigraph sampling by randomly selecting the graph on which to walk at each iteration. We demonstrate the benefits of our approach through (i) simulation in synthetic graphs, and (ii) measurements of Last.fm- an Internet website for music with social networking features. More specifically, we show that multigraph sampling can obtain a representative sample and faster convergence, even when the individual graphs fail, i.e., are disconnected or highly clustered.

Warning tweets: serial transmission of messages during the warning phase of a disaster event

Serial transmission – the passing on of information from one source to another – is a phenomenon of central interest in the study of informal communication in emergency settings. Microblogging services such as Twitter make it possible to study serial transmission on a large scale and to examine the factors that make retransmission of messages more or less likely. Here, we consider factors predicting serial transmission at the interface of formal and informal communication during disaster; specifically, we examine the retransmission by individuals of messages (tweets) issued by formal organizations on Twitter. Our central question is the following: How do message content, message style, and public attention to tweets relate to the behavioral activity of retransmitting (i.e. retweeting) a message in disaster? To answer this question, we collect all public tweets sent by a set of official government accounts during a 48-hour period of the Waldo Canyon wildfire. We manually code tweets for their thematic content and elements of message style. We then create predictive models to show how thematic content, message style, and changes in number of Followers affect retweeting behavior. From these predictive models, we identify the key elements that affect public retransmission of messages during the emergency phase of an unfolding disaster. Our findings suggest strategies for designing and disseminating messages through networked social media under periods of imminent threat.

The complexity of social networks : theoretical and empirical findings

Abstract A great deal of work in recent years has been devoted to the topic of “complexity”, its measurement, and its implications. Here, the notion of algorithmic complexity is applied to the analysis of social networks. Structural features of theoretical importance — such as structural equivalence classes — are shown to be strongly related to the algorithmic complexity of graphs, and these results are explored using analytical and simulation methods. Analysis of the complexity of a variety of empirically derived networks suggests that many social networks are nearly as complex as their source entropy, and thus that their structure is roughly in line with the conditional uniform graph distribution hypothesis. Implications of these findings for network theory and methodology are also discussed.

Geographical variability and network structure

Abstract In this paper, we explore the potential implications of geographical variability for the structure of social networks. Beginning with some basic simplifying assumptions, we derive a number of ways in which local network structure should be expected to vary across a region whose population is unevenly distributed. To examine the manner in which these effects would be expected to manifest given realistic population distributions, we then perform an exploratory simulation study that examines the features of large-scale interpersonal networks generated using block-level data from the 2000 U.S. Census. Using a stratified sample of micropolitan and metropolitan areas with populations ranging from approximately 1000 to 1,000,000 persons, we extrapolatively simulate network structure using spatial network models calibrated to two fairly proximate social relations. From this sample of simulated networks, we examine the effect of both within-location and between-location heterogeneity on a variety of structural properties. As we demonstrate, geographical variability produces large and distinctive features in the “social fabric” that overlies it; at the same time, however, many aggregate network properties can be fairly well-predicted from relatively simple spatial demographic variables. The impact of geographical variability is thus predicted to depend substantially on the type of network property being assessed, and on the spatial scale involved.

Responder Communication Networks in the World Trade Center Disaster: Implications for Modeling of Communication Within Emergency Settings

Using archival materials obtained from the Port Authority of New York and New Jersey, we analyze networks of communication and interaction among responders to the World Trade Center disaster. Our findings indicate substantial variability in individual radio communication system usage, with both communication volume and number of partners exhibiting distributions with long upper tails. Responder communication patterns are well-described by a fairly simple four-role structure and exhibit substantial similarity across responder groups (both specialist and non-specialist). Occupancy of coordinating roles is influenced by formal institutional status, but the vast majority of hub role occupancy appears to be emergent in character. Examination of both radio transcripts and police reports suggests that much of the communication among WTC responders is centered on problems of spatial reasoning and peer location, possibly providing an explanation for the importance of improvised coordination at the event site. Although these problems appear to have posed substantial challenges for responders at Ground Zero, we find the global communication/interaction network among Port Authority officers to be fairly well-connected, with little evidence of large-scale fragmentation (despite perceptions to the contrary). Implications of these findings for the modeling of communication networks in emergency settings are discussed.