Intrinsically Dynamic Network Communities

Community finding algorithms for networks have recently been extended to dynamic data. Most of these recent methods aim at exhibiting community partitions from successive graph snapshots and thereafter connecting or smoothing these partitions using clever time-dependent features and sampling techniques. These approaches are nonetheless achieving longitudinal rather than dynamic community detection. We assume that communities are fundamentally defined by the repetition of interactions among a set of nodes over time. According to this definition, analyzing the data by considering successive snapshots induces a significant loss of information: we suggest that it blurs essentially dynamic phenomena - such as communities based on repeated inter-temporal interactions, nodes switching from a community to another across time, or the possibility that a community survives while its members are being integrally replaced over a longer time period. We propose a formalism which aims at tackling this issue in the context of time-directed datasets (such as citation networks), and present several illustrations on both empirical and synthetic dynamic networks. We eventually introduce intrinsically dynamic metrics to qualify temporal community structure and emphasize their possible role as an estimator of the quality of the community detection - taking into account the fact that various empirical contexts may call for distinct `community' definitions and detection criteria.Comment: 27 pages, 11 figure

Laggard Clusters as Slow Learners, Emerging Clusters as Locus of Knowledge Cohesion (and Exclusion): A Comparative Study in the Wine Industry

This paper adopts sociometric analysis to explore the process of knowledge acquisition and diffusion in clusters of firms. By comparing the knowledge systems of two clusters selected for being at different stages of their development path, this study shows that the knowledge system of the laggard clusterbis weak, highly disconnected and vulnerable, while in the case of the emerging, dynamic cluster, the knowledge system is characterized by a more connected yet uneven knowledge acquisition and distribution process. These differences are then interpreted considering the heterogeneity of firm knowledge bases across and within clusters and the impact of this latter variable on the degree of intra- and extra-cluster connectivity is explored.Clusters, Firm Knowledge Base, Knowledge Systems, Social Network Analysis

Exploring the Evolution of Node Neighborhoods in Dynamic Networks

Dynamic Networks are a popular way of modeling and studying the behavior of evolving systems. However, their analysis constitutes a relatively recent subfield of Network Science, and the number of available tools is consequently much smaller than for static networks. In this work, we propose a method specifically designed to take advantage of the longitudinal nature of dynamic networks. It characterizes each individual node by studying the evolution of its direct neighborhood, based on the assumption that the way this neighborhood changes reflects the role and position of the node in the whole network. For this purpose, we define the concept of \textit{neighborhood event}, which corresponds to the various transformations such groups of nodes can undergo, and describe an algorithm for detecting such events. We demonstrate the interest of our method on three real-world networks: DBLP, LastFM and Enron. We apply frequent pattern mining to extract meaningful information from temporal sequences of neighborhood events. This results in the identification of behavioral trends emerging in the whole network, as well as the individual characterization of specific nodes. We also perform a cluster analysis, which reveals that, in all three networks, one can distinguish two types of nodes exhibiting different behaviors: a very small group of active nodes, whose neighborhood undergo diverse and frequent events, and a very large group of stable nodes

Static and Dynamic Aspects of Scientific Collaboration Networks

Collaboration networks arise when we map the connections between scientists which are formed through joint publications. These networks thus display the social structure of academia, and also allow conclusions about the structure of scientific knowledge. Using the computer science publication database DBLP, we compile relations between authors and publications as graphs and proceed with examining and quantifying collaborative relations with graph-based methods. We review standard properties of the network and rank authors and publications by centrality. Additionally, we detect communities with modularity-based clustering and compare the resulting clusters to a ground-truth based on conferences and thus topical similarity. In a second part, we are the first to combine DBLP network data with data from the Dagstuhl Seminars: We investigate whether seminars of this kind, as social and academic events designed to connect researchers, leave a visible track in the structure of the collaboration network. Our results suggest that such single events are not influential enough to change the network structure significantly. However, the network structure seems to influence a participant's decision to accept or decline an invitation.Comment: ASONAM 2012: IEEE/ACM International Conference on Advances in Social Networks Analysis and Minin

Evolutionary Events in a Mathematical Sciences Research Collaboration Network

This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this study traces the evolution of the "here and now" using fixed-duration sliding windows. The analysis uses a suite of common network diagnostics, including the distributions of degrees, distances, and clustering, to track network structure. Several random models that call these diagnostics as parameters help tease them apart as factors from the values of others. Some behaviors are consistent over the entire interval, but most diagnostics indicate that the network's structural evolution is dominated by occasional dramatic shifts in otherwise steady trends. These behaviors are not distributed evenly across the network; stark differences in evolution can be observed between two major subnetworks, loosely thought of as "pure" and "applied", which approximately partition the aggregate. The paper characterizes two major events along the mathematics network trajectory and discusses possible explanatory factors.Comment: 30 pages, 14 figures, 1 table; supporting information: 5 pages, 5 figures; published in Scientometric

Span-core Decomposition for Temporal Networks: Algorithms and Applications

When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high density holds). In this paper we tackle this task by introducing a notion of temporal core decomposition where each core is associated with two quantities, its coreness, which quantifies how densely it is connected, and its span, which is a temporal interval: we call such cores \emph{span-cores}. For a temporal network defined on a discrete temporal domain $T$, the total number of time intervals included in $T$ is quadratic in $|T|$, so that the total number of span-cores is potentially quadratic in $|T|$ as well. Our first main contribution is an algorithm that, by exploiting containment properties among span-cores, computes all the span-cores efficiently. Then, we focus on the problem of finding only the \emph{maximal span-cores}, i.e., span-cores that are not dominated by any other span-core by both their coreness property and their span. We devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly extract the maximal ones without computing all span-cores. Finally, as a third contribution, we introduce the problem of \emph{temporal community search}, where a set of query vertices is given as input, and the goal is to find a set of densely-connected subgraphs containing the query vertices and covering the whole underlying temporal domain $T$. We derive a connection between this problem and the problem of finding (maximal) span-cores. Based on this connection, we show how temporal community search can be solved in polynomial-time via dynamic programming, and how the maximal span-cores can be profitably exploited to significantly speed-up the basic algorithm.Comment: ACM Transactions on Knowledge Discovery from Data (TKDD), 2020. arXiv admin note: substantial text overlap with arXiv:1808.0937