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Eigenvector Centrality

The Eigenvector Centrality is a centrality measure that takes into account the importance (both in weighted or unweighted networks) of the selected node and also the importance of his neighbors in the network. Well connected nodes that also connect to well-connected nodes have higher Eigenvector Centrality. It is defined as the components of the eigenvector of the adjacency matrix with the largest eigenvalue. We normalize the Eigenvector components to a maximum value of 1. This centrality measure tends to highlight a few important nodes, assigning a value close to zero to most of the other nodes.

BeGraph uses the well-known power method to calculate the Eigenvector. Indeed, it may present convergence problems if the network is directed because the adjacency matrix is no longer symmetric and lacks useful algebraic properties.

Input parameter Type Default Description
Iterations* int> 0 100 Number of iterations in the power method.
Link weight textNone Name of the link weight property to consider. Large numbers mean strong links. Must be positive numbers.

* Required Field

We illustrate this centrality in the following plots. In the left network, the Eigenvector Centrality points to the red node as the most central node in the network. Orange and greenindicate medium values of this centrality, and blue/purple mean close to zero. In the right-hand side plot, we choose the color scheme to highlight a region of the network as the most important according to the Eigenvector Centrality.



References:

  • M.E.J. Newman, Networks, an introduction, Oxford University Press, 2010, ISBN: 978-0-19-920665-0, sec. 7.2.
algorithms/eigenvector.txt · Last modified: 2018/12/20 14:20 by systems