Random Walk on Multiple Networks

Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited information. In contrast, real data often contain entities with different types or/and from different sources, which are comprehensive and can be better modeled by multiple networks. To take advantage of rich information in multiple networks and make better inferences on entities, in this study, we propose random walk on multiple networks, RWM. RWM is flexible and supports both multiplex networks and general multiple networks, which may form many-to-many node mappings between networks. RWM sends a random walker on each network to obtain the local proximity (i.e., node visiting probabilities) w.r.t. the starting nodes. Walkers with similar visiting probabilities reinforce each other. We theoretically analyze the convergence properties of RWM. Two approximation methods with theoretical performance guarantees are proposed for efficient computation. We apply RWM in link prediction, network embedding, and local community detection. Comprehensive experiments conducted on both synthetic and real-world datasets demonstrate the effectiveness and efficiency of RWM.Comment: Accepted to IEEE TKD

The Minimum Wiener Connector

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$ of query vertices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. We show that The Minimum Wiener Connector admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless $\mathbf{P} = \mathbf{NP}$. Our main contribution is a constant-factor approximation algorithm running in time $\widetilde{O}(|Q||E|)$. A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set $Q$ a small number of important vertices (i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International Conference on Management of Dat

Large Graph Analysis in the GMine System

Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed in an interactive environment, where human expertise can guide the process. For large graphs, though, there are some challenges: the excessive processing requirements are prohibitive, and drawing hundred-thousand nodes results in cluttered images hard to comprehend. To cope with these problems, we propose an innovative framework suited for any kind of tree-like graph visual design. GMine integrates (a) a representation for graphs organized as hierarchies of partitions - the concepts of SuperGraph and Graph-Tree; and (b) a graph summarization methodology - CEPS. Our graph representation deals with the problem of tracing the connection aspects of a graph hierarchy with sub linear complexity, allowing one to grasp the neighborhood of a single node or of a group of nodes in a single click. As a proof of concept, the visual environment of GMine is instantiated as a system in which large graphs can be investigated globally and locally