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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.

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Citations
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Analysis of Dynamic Community Detection Algorithm

TL;DR: This work focuses on methods of identifying dynamic communities in association with other parameters in interaction network which may analyse community effectively.
Book ChapterDOI

Fast Algorithms for Constrained Graph Density Problems

TL;DR: This work considers the question of finding communities in large social networks and looks at the minimum degree of a subgraph as a measure of the connectedness of the community.
Journal ArticleDOI

Finding a Friendly Community in Social Networks Considering Bad Relationships

TL;DR: This paper proposes a new variant of the community detection problem, called friendly community search, and proves that Non-deterministic Polynomial-time hard (NP-hard), and develops two novel algorithms, called Greedy and SteinerSwap that return the near optimal solutions.

S ubquadratic a lgorithms for k ernel m atri - ces via k ernel d ensity e stimation

Ainesh Bakshi, +1 more
TL;DR: In this article , a 41x reduction in the graph size for spectral sparsification was reported. But the number of kernel evaluations over baselines for LRA was not significantly reduced.
Journal ArticleDOI

Mediation analysis for high-dimensional mediators and outcomes with an application to multimodal imaging data

TL;DR: In this article , a novel multivariate mediator and multivariate-outcome mediation model (MMO) is proposed to simultaneously extract the latent systematic mediation patterns and estimate the mediation effects based on a dense bi-cluster graph approach.
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.
Journal ArticleDOI

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.
Trending Questions (1)
Calculate the density of directed and undirected graph?

The density of a directed graph is defined as the maximum density of any subset of vertices, while the density of an undirected graph is defined as the maximum density of any subset of vertices.