Distance Preserving Graph Simplification

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph. Specifically, we construct a gate graph from a large graph so that for any "non-local" vertex pair (distance higher than some threshold) in the original graph, their shortest-path distance can be recovered by consecutive "local" walks through the gate vertices in the gate graph. We perform a theoretical investigation on the gate-vertex set discovery problem. We characterize its computational complexity and reveal the upper bound of minimum gate-vertex set using VC-dimension theory. We propose an efficient mining algorithm to discover a gate-vertex set with guaranteed logarithmic bound. We further present a fast technique for pruning redundant edges in a gate graph. The detailed experimental results using both real and synthetic graphs demonstrate the effectiveness and efficiency of our approach.Comment: A short version of this paper will be published for ICDM'11, December 201

Bisecting for selecting: using a Laplacian eigenmaps clustering approach to create the new European football Super League

Ranking sports teams generally relies on supervised techniques, requiring either prior knowledge or arbitrary metrics. In this paper, we offer a purely unsupervised technique. We apply this to operational decision-making, specifically, the controversial European Super League for associa-tion football, demonstrating how this approach can select dominant teams to form the new league. We first use random forest regression to select important variables predicting goal difference, which we use to calculate the Euclidian distances between teams. Creating a Laplacian eigenmap, we bisect the Fiedler vector to identify the natural clusters in five major European football leagues. Our results show how an unsupervised approach could identify four clusters based on five basic performance metrics: shots, shots on target, shots conceded, possession, and pass success. The top two clusters identify teams that dominate their respective leagues and are the best candidates to create the most competitive elite super league

Algorithms for the visualization and simulation of mobile ad hoc and cognitive networks

Visualization and simulation are important aspects of most advanced engineering endeavors. They may provide important insights into the functionality and perfor- mance of a system during the design and evaluation stage of the system's development. This thesis presents a number of algorithms and simulation algorithms that may be used for the design and evaluation of two types of engineered systems, mobile ad hoc and cognitive networks. The ¯rst set of algorithms provides signal radiation pattern and digital terrain visualization capabilities to OMAN, a mobile ad hoc network sim- ulator developed at Drexel University. The second set of algorithms provides a more general visualization capability for displaying complex graphs. These algorithms fo- cus on simplifying a complex graph in order to allow a user to explore its underlying basic structure. The thesis closes with a description of a GPU-based implementation of a set of spectrum-sensing algorithms. Spectrum sensing is an important function- ality needed for cognitive networks. The computational speed-ups provided by the GPU implementation o®er the possibility of real-time spectrum-sensing for adaptive, cognitive networks.M.S., Computer Science -- Drexel University, 200

Graph similarity and matching

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 85-88).Measures of graph similarity have a broad array of applications, including comparing chemical structures, navigating complex networks like the World Wide Web, and more recently, analyzing different kinds of biological data. This thesis surveys several different notions of similarity, then focuses on an interesting class of iterative algorithms that use the structural similarity of local neighborhoods to derive pairwise similarity scores between graph elements. We have developed a new similarity measure that uses a linear update to generate both node and edge similarity scores and has desirable convergence properties. This thesis also explores the application of our similarity measure to graph matching. We attempt to correctly position a subgraph GB within a graph GA using a maximum weight matching algorithm applied to the similarity scores between GA and GB. Significant performance improvements are observed when the topological information provided by the similarity measure is combined with additional information about the attributes of the graph elements and their local neighborhoods. Matching results are presented for subgraph matching within randomly-generated graphs; an appendix briefly discusses matching applications in the yeast interactome, a graph representing protein-protein interactions within yeast.by Laura Zager.S.M