Finding and Testing Network Communities by Lumped Markov Chains

Finding and Testing Network Communities by Lumped Markov Chains

Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov c...

Finding Generators for Markov Chains

Correction: Uncovering and Testing the Fuzzy Clusters Based on Lumped Markov Chain in Complex Network

Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the prop...

Finding the stationary states of Markov chains by iterative methods

Keywords: Google problem Power Method Stochastic matrices Global rate of convergence Gradient methods Strong convexity a b s t r a c t In this paper, we develop new methods for approximating dominant eigenvector of column-stochastic matrices. We analyze the Google matrix, and present an averaging scheme with linear rate of convergence in terms of 1-norm distance. For extending this convergence ...

Detecting Communities using Absorbing Markov Chains

Community detection is an important part of network analysis. The goal is simple: to detect how nodes in the graph ought to be grouped into communities. Some algorithms wholly partition the nodes; others allow for some nodes to be considered ”community-less”. Community detection has several applications: for example, suggesting connections (as in, say, Facebook) and determining network structur...