Entropy of dialogues creates coherent structures in e-mail traffic

Abstract

We study the dynamic network of e-mail traffic and find that it develops self-organized coherent structures similar to those appearing in many nonlinear dynamic systems. Such structures are uncovered by a general information theoretic approach to dynamic networks based on the analysis of synchronization among trios of users. In the e-mail network, coherent structures arise from temporal correlations when users act in a synchronized manner. These temporally linked structures turn out to be functional, goal-oriented aggregates that must react in real time to changing objectives and challenges (e.g., committees at a university). In contrast, static structures turn out to be related to organizational units (e.g., departments).A n intriguing aspect of networks is the appearance of internal structures whose origins cannot be explained by using graph theoretic concepts alone. These are contextual and thematic groups that form by the clustering of nodes with similar properties. Their existence can be detected by various measures of connectivity (1-3), and they have numerous uses in data mining (4). The addition of temporal dynamics can be expected to have a profound effect on the creation of such structures. The time-dependent activation of links creates a flow of information along the static network that, in turn, defines an ever-changing subgraph that can only exist as a consequence of this flow. This flux of activation will concentrate and cluster into structures that act coherently for a given period, then relax and decay until they are excited again.A dynamic network can be defined as a graph whose links are turned on or off by the individual nodes. Prominent examples are the brain, where spikes are exchanged among neurons to create thoughts, and communication networks such as telephones or e-mail. It is convenient to think of the static counterpart as the same graph in which permanent links are made when certain criteria are fulfilled, e.g., when the number of messages transmitted between two nodes exceeds a certain threshold level. The temporal dynamics create coherent space-time structures that involve correlations of the interacting nodes. These (coherent and dynamic) structures will in general be very different from the fixed ones that appear in the static network.E-mail traffic, a fascinating form of communication that increasingly dominates written correspondence, creates such a dynamic network. The resulting graph has intricate structures that are neither apparent to the users nor carried by the content of the messages. The traffic has a precise time stamp on every interaction, which can be used as a ''stroboscopic probe'' to identify the coherent space-time structures that arise. In this work, we measure synchronized interaction among users by looking at communicating triangles of users. We analyze them with the tools of information theory (5) and find a form of organization that differs from that which can be captured by static attributes of the graph such as curvature. A similar approach is often used to...

Temporal networks

“…regarding durations of time-respecting paths and latencies between vertices. Especially, for temporal networks of human communication, it has been discovered that such timings are often bursty and deviate from the more uniform times expected from a memoryless, random Poisson process [7,21,39,61,69,71,102,107,115,157,162]. Overall, the burstiness manifests itself in broader-than-expected distributions of inter-contact times, P(τ), defined either for nodes or their individual edges.…”

“…Such data often come either in the form of lists of messages from one person to another at a point in time, or a dialogue between two persons within a time interval. The first type contains networks of e-mail messages [39,61,120,157], mobile phone text messages [162,169], and instant messages and messages in online forums [58,95]. Phone calls are not instantaneous but have a specific duration, and can thus be considered to be of the second type [21,71,107,116,120].…”

“…Further, assume that the person gets sick and infectious if the virus concentration reaches a critical level. Then, bursty edge dynamics [7,39,76,84,163] could be of crucial importance for that something to propagate through the network. In a situation with more uncorrelated or evenly distributed times of contact, the virus concentration would have time to fall below the dangerous level between the contacts.…”

Information flow in social groups

“…It pervades business, social and scientific exchanges and as such it is a highly relevant area for research on communities and social networks. Not surprisingly, email has been established as an indicator of collaboration and knowledge exchange [1,2,3,4,5]. Email is also a good medium for research because it provides plentiful data on personal communication in an electronic form.…”

Impact of interactions on human dynamics

“…In the recent years we have experienced an increased research activity in this area motivated by the increased availability of empirical data. We now count with measurements of human activities covering several individuals and several events per individual [3,4,5,6,7]. Thanks to this data we are in a position to investigate the laws and patterns of human dynamics using a scientific approach.…”