Abstract—Network vulnerability assessment is an indispensable component of attack risk reduction and proactive response. However, traditional assessment methods simply assume the attacks only target at nodes with high degree or betweenness centrality, thus fail to capture the worst-case scenarios under simultaneous failures. In our previous work, we formulated assessing network vulnerability as optimization problems, socalled β-edge disruptor and β-vertex disruptor, to identify the minimum cost critical infrastructures that removal expose the network to a certain disruption level. Here, the disruption is measured as the fraction of node pairs with no paths between them in the residual network. In this paper, we present an exact analytical solution for the vulnerability assessment problems i.e. an exact branch-and-cut algorithm to solve the integer programming formulation of the β-vertex disruptor. The two intriguing aspects of the algorithms are an efficient Mixed Integer Programming (MIP) formulation, called sparse metric, and vertex-cut inequalities, a specialized cutting plane procedure that tightens the bound on the optimal solutions. Experiments on both synthetic and real-world networks suggest that our algorithm yields a significant improvement on a large variety of network instances, raising the size of the largest instance solved from several dozen to several hundred nodes. Our techniques can be easily extended to many graph partitioning and connectivity optimization problems. I.

Virtual communities have become an important new organizational form and yet relatively little is known about the conditions which lead to their success. In an attempt to address this knowledge gap, a particular subset of virtual communities- open source software project communities- is investigated and four hypotheses are asserted which relate social network structure to community success. The hypotheses, which are based on social network theory and related research, suggest that success is supported by high levels of affiliation with other communities, moderate levels of density within the network of community conversations, moderate levels of density in the communications between peripheral members and core members, and low levels of density in the communications between administrators and the rest of the community. Empirical research is underway to test these hypotheses based on a sample of over 200 open source software project communities.

Abstract—Given a real world graph, how should we layout its edges? How can we compress it? These questions are closely related, and the typical approach so far is to find cliquelike communities, like the ‘cavemen graph’, and compress them. We show that the block-diagonal mental image of the ‘cavemen graph ’ is the wrong paradigm, in full agreement with earlier results that real world graphs have no good cuts. Instead, we propose to envision graphs as a collection of hubs connecting spokes, with super-hubs connecting the hubs, and so on, recursively. Based on the idea, we propose the SLASHBURN method (burn the hubs, and slash the remaining graph into smaller connected components). Our view point has several advantages: (a) it avoids the ‘no good cuts ’ problem, (b) it gives better compression, and (c) it leads to faster execution times for matrix-vector operations, which are the back-bone of most graph processing tools. Experimental results show that our SLASHBURN method consistently outperforms other methods on all datasets, giving good compression and faster running time.

Node centrality measures are important in a large number of graph applications, from search and ranking to social and biological network analysis. In this paper we study node centrality for very large graphs, up to billions of nodes and edges. Various definitions for centrality have been proposed, ranging from very simple (e.g., node degree) to more elaborate. However, measuring centrality in billion-scale graphs poses several challenges. Many of the “traditional ” definitions such as closeness and betweenness were not designed with scalability in mind. Therefore, it is very difficult, if not impossible, to compute them both accurately and efficiently. In this paper, we propose centrality measures suitable for very large graphs, as well as scalable methods to effectively compute them. More specifically, we propose effective closeness and LINERANK which are designed for billion-scale graphs. We also develop algorithms to compute the proposed centrality measures in MAPREDUCE, a modern paradigm for large-scale, distributed data processing. We present extensive experimental results on both synthetic and real datasets, which demonstrate the scalability of our approach to very large graphs, as well as interesting findings and anomalies. 1