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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

(p.108) (p.109) 6 Communicability functions in networks
The Structure of Complex Networks

Ernesto Estrada

Oxford University Press

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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