Molecular Model of Dynamic Social Network Based on E-mail communication

In this work we consider an application of physically inspired sociodynamical model to the modelling of the evolution of email-based social network. Contrary to the standard approach of sociodynamics, which assumes expressing of system dynamics with heuristically defined simple rules, we postulate the inference of these rules from the real data and their application within a dynamic molecular model. We present how to embed the n-dimensional social space in Euclidean one. Then, inspired by the Lennard-Jones potential, we define a data-driven social potential function and apply the resultant force to a real e-mail communication network in a course of a molecular simulation, with network nodes taking on the role of interacting particles. We discuss all steps of the modelling process, from data preparation, through embedding and the molecular simulation itself, to transformation from the embedding space back to a graph structure. The conclusions, drawn from examining the resultant networks in stable, minimum-energy states, emphasize the role of the embedding process projecting the non–metric social graph into the Euclidean space, the significance of the unavoidable loss of information connected with this procedure and the resultant preservation of global rather than local properties of the initial network. We also argue applicability of our method to some classes of problems, while also signalling the areas which require further research in order to expand this applicability domain

Scalable Online Betweenness Centrality in Evolving Graphs

Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best known algorithm runs in O(nm) time. The problems of efficiency and scalability are exacerbated in a dynamic setting, where the input is an evolving graph seen edge by edge, and the goal is to keep the betweenness centrality up to date. In this paper we propose the first truly scalable algorithm for online computation of betweenness centrality of both vertices and edges in an evolving graph where new edges are added and existing edges are removed. Our algorithm is carefully engineered with out-of-core techniques and tailored for modern parallel stream processing engines that run on clusters of shared-nothing commodity hardware. Hence, it is amenable to real-world deployment. We experiment on graphs that are two orders of magnitude larger than previous studies. Our method is able to keep the betweenness centrality measures up to date online, i.e., the time to update the measures is smaller than the inter-arrival time between two consecutive updates.Comment: 15 pages, 9 Figures, accepted for publication in IEEE Transactions on Knowledge and Data Engineerin

On Graph Stream Clustering with Side Information

Graph clustering becomes an important problem due to emerging applications involving the web, social networks and bio-informatics. Recently, many such applications generate data in the form of streams. Clustering massive, dynamic graph streams is significantly challenging because of the complex structures of graphs and computational difficulties of continuous data. Meanwhile, a large volume of side information is associated with graphs, which can be of various types. The examples include the properties of users in social network activities, the meta attributes associated with web click graph streams and the location information in mobile communication networks. Such attributes contain extremely useful information and has the potential to improve the clustering process, but are neglected by most recent graph stream mining techniques. In this paper, we define a unified distance measure on both link structures and side attributes for clustering. In addition, we propose a novel optimization framework DMO, which can dynamically optimize the distance metric and make it adapt to the newly received stream data. We further introduce a carefully designed statistics SGS(C) which consume constant storage spaces with the progression of streams. We demonstrate that the statistics maintained are sufficient for the clustering process as well as the distance optimization and can be scalable to massive graphs with side attributes. We will present experiment results to show the advantages of the approach in graph stream clustering with both links and side information over the baselines.Comment: Full version of SIAM SDM 2013 pape

Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work