Book ChapterDOI
Greedy approximation algorithms for finding dense components in a graph
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TLDR
This paper gives simple greedy approximation algorithms for these optimization problems of finding subgraphs maximizing these notions of density for undirected and directed graphs and answers an open question about the complexity of the optimization problem for directed graphs.Abstract:
We study the problem of finding highly connected subgraphs of undirected and directed graphs. For undirected graphs, the notion of density of a subgraph we use is the average degree of the subgraph. For directed graphs, a corresponding notion of density was introduced recently by Kannan and Vinay. This is designed to quantify highly connectedness of substructures in a sparse directed graph such as the web graph. We study the optimization problems of finding subgraphs maximizing these notions of density for undirected and directed graphs. This paper gives simple greedy approximation algorithms for these optimization problems. We also answer an open question about the complexity of the optimization problem for directed graphs.read more
Citations
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Journal ArticleDOI
Parallel Maximum Clique Algorithms with Applications to Network Analysis
TL;DR: A fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks and employs a branch-and-bound strategy with novel and aggressive pruning techniques.
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Scalable Anomaly Ranking of Attributed Neighborhoods
Bryan Perozzi,Leman Akoglu +1 more
TL;DR: Normality as mentioned in this paper is a new quality measure for attributed neighborhoods, which utilizes structure and attributes together to quantify both internal consistency and external separability, and can be efficiently maximized to automatically infer the shared attribute subspace (and respective weights) that characterize a neighborhood.
Journal ArticleDOI
Spectral Properties of Hypergraph Laplacian and Approximation Algorithms
TL;DR: This article introduces a new hypergraph Laplacian operator, induced by a diffusion process on the hypergraph, and gives a polynomial-time algorithm to compute an O(log r)-approximation to the kth procedural minimizer, where r is the maximum cardinality of a hyperedge.
Proceedings ArticleDOI
Dense Subgraph Discovery: KDD 2015 tutorial
TL;DR: This tutorial aims to provide a comprehensive overview of major algorithmic techniques for finding dense subgraphs in large graphs and graph mining applications that rely on dense sub graph extraction, as well as the latest advances in the area, from theoretical and from practical point-of-view.
Proceedings ArticleDOI
Locally Densest Subgraph Discovery
TL;DR: It is shown that the set of locally densest subgraphs in a graph can be computed in polynomial time and three novel pruning strategies are proposed to largely reduce the search space of the algorithm.
References
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Proceedings ArticleDOI
Authoritative sources in a hyperlinked environment
TL;DR: This work proposes and test an algorithmic formulation of the notion of authority, based on the relationship between a set of relevant authoritative pages and the set of \hub pages that join them together in the link structure, that has connections to the eigenvectors of certain matrices associated with the link graph.
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Trawling the Web for emerging cyber-communities
TL;DR: The subject of this paper is the systematic enumeration of over 100,000 emerging communities from a Web crawl, motivating a graph-theoretic approach to locating such communities, and describing the algorithms and algorithmic engineering necessary to find structures that subscribe to this notion.
Book ChapterDOI
The web as a graph: measurements, models, and methods
TL;DR: This paper describes two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery, and proposes a new family of random graph models that point to a rich new sub-field of the study of random graphs, and raises questions about the analysis of graph algorithms on the Internet.
Proceedings ArticleDOI
Inferring Web communities from link topology
TL;DR: This investigation shows that although the process by which users of the Web create pages and links is very difficult to understand at a “local” level, it results in a much greater degree of orderly high-level structure than has typically been assumed.