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Computing the Probability Vectors for Random Walks on Graphs with Bounded Arboricity

Gaurav Goel 1, 2
1 ALGORILLE - Algorithms for the Grid
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The problem of detecting dense subgraphs (\emph{communities}) in large sparse graphs is inherent to many real world domains like social networking. A popular approach of detecting these communities involves first computing the \emph{probability~vectors} for \emph{random~walks} on the graph for a fixed number of steps, and then using these probability vectors to detect the communities. Such an approach has been discussed by Latapy and Pons in \cite{latapypons}. They compute the probability vectors using simple matrix multiplication and define a measure of the structural similarity between vertices which they call \emph{distance}. Based on the probability vectors, they compute the distances between vertices and then based on these distances group the vertices into communities. Their algorithm takes $O(n^2\log n)$ time where $n$ is the number of vertices in the graph. We focus on the first part of the approach i.e. computation of the probability vectors for the random walks, and propose a more efficient algorithm (than matrix multiplication) for computing these vectors in time complexity that is linear in the size of the output.
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Submitted on : Friday, November 4, 2005 - 9:58:31 AM
Last modification on : Friday, February 26, 2021 - 3:28:02 PM
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Gaurav Goel. Computing the Probability Vectors for Random Walks on Graphs with Bounded Arboricity. [Internship report] 2005. ⟨inria-00000578⟩

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