Variations in Graph Energy: A Measure for Network Resilience

Abstract

There are many models and metrics developed to study the resilience of networks. Eigenvalues are the roots of the characteristic polynomial for a given graph and are mathematically rigorous compared to a statistical measure such as degree distribution. The graph energy is the sum of absolute values of eigenvalues; there is a subtle difference between the adjacency, Laplacian, and normalized Laplacian graph energy calculations. Our primary objective in this paper is to understand what different graph energy mean from a network resilience point of view. We calculate the adjacency, Laplacian, and normalized Laplacian graph energies on four backbone networks under targeted node and link attack scenarios. While adjacency and Laplacian graph energy decrease with node and link attacks, the normalized Laplacian energy increases with link attacks converging to a maximum value equal to the network order. The structural similarities of physical-level topologies is revealed by the close values of adjacency and Laplacian energies.

Meeting Name

9th International Workshop on Resilient Networks Design and Modeling, RNDM 2017 (2017, Sep. 4-6, Alghero, Italy)

Department(s)

Electrical and Computer Engineering

Keywords and Phrases

Eigenvalues and eigenfunctions; Laplace transforms; Adjacency energy; Attack; Back-bone network; Betweenness; Closeness; Degree; Eigen-value; Graph energy; Laplacians; Normalized Laplacian; Graph theory; Backbone network; Eigenvalue; Laplacian energy; Normalized Laplacian energy

International Standard Book Number (ISBN)

978-1-5386-0671-1

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Sep 2017

Link to Full Text

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