From centrality to temporary fame: Dynamic centrality in complex networks

Abstract

We develop a new approach to the study of the dynamics of link utilization in complex networks using records of communication in a large social network. Counter to the perspective that nodes have particular rolesKey Words: social networks, time-based networks, dynamic hubs, multiscale networks, turbulent networks R ecent advances have demonstrated that the study of universal properties in physical systems may be extended to complex networks in biological and social systems [1][2][3][4][5]. This has opened the study of such networks to experimental and theoretical characterization of properties and mechanisms of formation. In this article we extend the study of complex networks by considering the dynamics of the activity of network connections. Our analysis suggests that fundamentally new insights can be obtained from the dynamical behavior, including a dramatic time dependence of the role of nodes that is not apparent from static (time aggregated) analysis of node connectivity and network topology.We study the communication between 57,158 e-mail users based on data sampled over a period of 113 days from log files maintained by the e-mail server at a large university [6]. The time when an e-mail link is established between any pair of e-mail addresses is routinely registered in a server, enabling the analysis of the temporal dynamics of the interactions within the network. To consider only e-mails that reflect the flow of valuable information, spam and bulk mailings were excluded using a prefilter. There were 447,543 messages exchanged by the users during a 113-day observation. We report results obtained by treating the communications as an undirected network, where e-mail addresses are regarded as nodes and two nodes are linked if there is an e-mail communication between them. Analysis based on treating the network with asymmetric links (where a distinction is made between out-going links and incoming links) gave essentially equivalent results. From the temporal Correspondence to: Yaneer Bar-Yam,

Discussing Occupy Wall Street on Twitter: Longitudinal Network Analysis of Equality, Emotion, and Stability of Public Discussion

“…Braha et al find that node centrality changes dramatically every day; thus, they suggest adopting dynamic centrality and dynamic network instead of static centrality and an aggregated network. 38 Equality of participation is measured based on the degree of nodes. We fit the power law distribution of node degree and test goodness of fit following the method proposed by Clauset et al 22 Stability is measured in two ways: (1) by calculating node centrality and analyzing the correlation matrix of individuals' participation in online discussion over 16 time windows and (2) by calculating the standard deviations for each individual's participation over time.…”

Molecular model of dynamic social network based on e-mail communication

“…There are some approaches that aim at developing specific models for online social networks and take into consideration some information characteristic to such networks [29], [30], [9], [8], [31], [12], [25]. Different models propose different methods of network growth.…”

“…A set of approaches that take into consideration the fact that links can disappear from the network have been proposed in [19,8] where the authors have detected a dramatic time dependance in network centrality and the role of nodes, something not apparent from static analysis of node connectivity and network topology. Their experiments studied a large-scale email networks consisting of 57,000 users based on data gathered over a period of 113 days.…”

Visual Analysis of Dynamic Networks Using Change Centrality

“…Other approaches consider the time series of static centrality metrics measured over subsequent time windows (e.g. daily or monthly), and compute basic statistics [14], [15]. In general, new metrics have been proposed for multidimensional networks, in which the attributes of nodes and links chosen as dimensions are not necessarily referring to time, but for example to the type of relation in multi-relational networks.…”