Random walk centrality for temporal networks

Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included

A Markov model for inferring flows in directed contact networks

Directed contact networks (DCNs) are a particularly flexible and convenient class of temporal networks, useful for modeling and analyzing the transfer of discrete quantities in communications, transportation, epidemiology, etc. Transfers modeled by contacts typically underlie flows that associate multiple contacts based on their spatiotemporal relationships. To infer these flows, we introduce a simple inhomogeneous Markov model associated to a DCN and show how it can be effectively used for data reduction and anomaly detection through an example of kernel-level information transfers within a computer.Comment: 12 page

Burstiness and tie activation strategies in time-varying social networks

The recent developments in the field of social networks shifted the focus from static to dynamical representations, calling for new methods for their analysis and modelling. Observations in real social systems identified two main mechanisms that play a primary role in networks' evolution and influence ongoing spreading processes: the strategies individuals adopt when selecting between new or old social ties, and the bursty nature of the social activity setting the pace of these choices. We introduce a time-varying network model accounting both for ties selection and burstiness and we analytically study its phase diagram. The interplay of the two effects is non trivial and, interestingly, the effects of burstiness might be suppressed in regimes where individuals exhibit a strong preference towards previously activated ties. The results are tested against numerical simulations and compared with two empirical datasets with very good agreement. Consequently, the framework provides a principled method to classify the temporal features of real networks, and thus yields new insights to elucidate the effects of social dynamics on spreading processes

Social Entrepreneurship: Role of Networks in Capturing Opportunities.

Social entrepreneurship, an exercise that amalgamates non-profit operations and business values in quest of social impact, has the ability to empower lots of individuals around the world in social problem-solving. This article investigates how managerial ties assist social entrepreneurs in discovering and capturing opportunities for their course. We also look at the moderating effect of centrality on the relationship between the social entrepreneur, managerial ties and opportunity. Drawing a sample from 300 social entrepreneurs, we recorded that, business ties have a more positive effect on opportunity and both degree and betweenness centrality positively moderates this relationship. However, social entrepreneurs are encouraged to establish ties with both government and business because they have different services to offer. But that notwithstanding, they are encouraged to have more business ties to discover and capture opportunities. Keywords: Social Entrepreneurship, government ties, business ties, opportunity capture. DOI: 10.7176/JRDM/53-06 Publication date:March 31st 201

What’s next in complex networks? Capturing the concept of attacking play in invasive team sports

The evolution of performance analysis within sports sciences is tied to technology development and practitioner demands. However, how individual and collective patterns self-organize and interact in invasive team sports remains elusive. Social network analysis has been recently proposed to resolve some aspects of this problem, and has proven successful in capturing collective features resulting from the interactions between team members as well as a powerful communication tool. Despite these advances, some fundamental team sports concepts such as an attacking play have not been properly captured by the more common applications of social network analysis to team sports performance. In this article, we propose a novel approach to team sports performance centered on sport concepts, namely that of an attacking play. Network theory and tools including temporal and bipartite or multilayered networks were used to capture this concept. We put forward eight questions directly related to team performance to discuss how common pitfalls in the use of network tools for capturing sports concepts can be avoided. Some answers are advanced in an attempt to be more precise in the description of team dynamics and to uncover other metrics directly applied to sport concepts, such as the structure and dynamics of attacking plays. Finally, we propose that, at this stage of knowledge, it may be advantageous to build up from fundamental sport concepts toward complex network theory and tools, and not the other way around.info:eu-repo/semantics/acceptedVersio

Eigenvector-Based Centrality Measures for Temporal Networks

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NTxNT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.Comment: 38 pages, 7 figures, and 5 table

Structural importance and evolution: an application to financial transaction networks

A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static networks, that do not change over time, but does not consider the dynamics of the network. Here we propose instead to measure the importance of a node based on how much a change to its strength will impact the global structure of the network, which we measure in terms of the spectrum of its adjacency matrix. We apply our method to the identification of important nodes in equity transaction networks and show that, while it can still be computed from a static network, our measure is a good predictor of nodes subsequently transacting. This implies that static representations of temporal networks can contain information about their dynamics