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Open AccessProceedings Article

Randomization Techniques for Graphs

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TLDR
This paper focuses on randomization techniques for unweighted undirected graphs for graph mining within the framework of statistical hypothesis testing, and describes three alternative algorithms based on local edge swapping and Metropolis sampling.
Abstract
Mining graph data is an active research area Several data mining methods and algorithms have been proposed to identify structures from graphs; still, the evaluation of those results is lacking Within the framework of statistical hypothesis testing, we focus in this paper on randomization techniques for unweighted undirected graphs Randomization is an important approach to assess the statistical significance of data mining results Given an input graph, our randomization method will sample data from the class of graphs that share certain structural properties with the input graph Here we describe three alternative algorithms based on local edge swapping and Metropolis sampling We test our framework with various graph data sets and mining algorithms for two applications, namely graph clustering and frequent subgraph mining

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References
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Equation of state calculations by fast computing machines

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The Structure and Function of Complex Networks

Mark Newman
- 01 Jan 2003 - 
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Journal ArticleDOI

Monte Carlo Sampling Methods Using Markov Chains and Their Applications

TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.
Journal ArticleDOI

Community structure in social and biological networks

TL;DR: This article proposes a method for detecting communities, built around the idea of using centrality indices to find community boundaries, and tests it on computer-generated and real-world graphs whose community structure is already known and finds that the method detects this known structure with high sensitivity and reliability.