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...
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.aggregation ͉ subgraphs A number of complex biological and nonbiological networks were recently found to contain network motifs, representing elementary interaction patterns between small groups of nodes (subgraphs) that occur substantially more often than would be expected in a random network of similar size and connectivity (1, 2). Theoretical and experimental evidence indicates that at least some of these recurring elementary interaction patterns carry significant information about the given network's function and overall organization (1-4). For example, transcriptional regulatory networks of cells (1, 2, 5, 6), neural networks of C. elegans (2), and some electronic circuits (2) are all information processing networks that contain a significant number of feed-forward loop (FFL) motifs. However, in transcriptional regulatory networks these motifs do not exist in isolation but meld into motif clusters (7), while other networks are devoid of FFLs altogether (2).In general, all subgraphs have two important properties: their topology and the directionality of their links. In cellular networks, these two properties can be clearly separated from each other. In protein-protein interaction (PPI) networks all links are by definition nondirectional. In contrast, in transcriptional regulatory networks information flow between a transcription factor and the operon (gene) regulated by it is almost always unidirectional (1, 2). Metabolic networks occupy an intermediate position between these two extremes, because most, but not all, metabolic reactions are reversible under various growth conditions. Despite the difference in the relative role of link directionality, the large-scale organization of the three different network types is quite similar, most being characterized by a scale-free connectivity distribution and hierarchical modularity (8-12). The only exception is the incoming degree distribution (i.e., the number of transcription factors regulating a target gene) of regulatory...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.