Abstract
Determining a set of “important” nodes in a network constitutes a basic endeavor in network science. Inspired by electrical flows in a resistor network, we propose the best conducting node in a graph as the minimizer of the diagonal element of the pseudoinverse matrix of the weighted Laplacian matrix of the graph . We propose a new graph metric that complements the effective graph resistance and that specifies the heterogeneity of the nodal spreading capacity in a graph. Various formulas and bounds for the diagonal element are presented. Finally, we compute the pseudoinverse matrix of the Laplacian of star, path, and cycle graphs and derive an expansion and lower bound of the effective graph resistance based on the complement of the graph .
- Received 9 March 2017
DOI:https://doi.org/10.1103/PhysRevE.96.032311
©2017 American Physical Society