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The Structure of Complex NetworksTheory and Applications$
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Ernesto Estrada

Print publication date: 2011

Print ISBN-13: 9780199591756

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199591756.001.0001

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Communicability functions in networks

Communicability functions in networks

Chapter:
(p.108) (p.109) 6 Communicability functions in networks
Source:
The Structure of Complex Networks
Author(s):

Ernesto Estrada

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199591756.003.0006

This chapter discusses the concept of communicability between a pair of nodes in a complex network and introduces a first measure of communicability on the basis of the exponential of the adjacency matrix of the network. It is interpreted as the thermal Green's function of the network, in which a ‘particle’ diffuses from one node to another because of a quantum dynamics. This concept is then extended to weighted and directed networks as well as to other matrix functions. Finally, the concept of communicability based on ‘vibrations’ of the nodes in a network is analysed. Examples of the physical analogies used here are presented.

Keywords:   communicability, thermal Green's function, vibrations, matrix functions, inverse Laplacian matrix

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