# The Eigenvectors of a Random Graph

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A graph can be represented by an adjacency matrix, with an entry of 1 at position if the node is connected to the node, and 0 otherwise. This Demonstration provides a visualization of the eigenvectors of the adjacency matrix of a graph. The eigenvalue is indicated above the graph. The size of the nodes (circles) are proportional to the absolute magnitude of that component of the eigenvector; the eigenvectors are related to the problem of graph partitioning. Yellow nodes indicate positive values and green nodes indicate negative values. The relative sizes of the nodes for a given eigenvalue indicate the relative importance (ranking of those nodes) as well as the community structure of the graph.

Contributed by: Michael Twardos (March 2011)

Open content licensed under CC BY-NC-SA

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"The Eigenvectors of a Random Graph"

http://demonstrations.wolfram.com/TheEigenvectorsOfARandomGraph/

Wolfram Demonstrations Project

Published: March 7 2011