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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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Accounting for all parts (subgraphs)

Accounting for all parts (subgraphs)

(p.89) 5 Accounting for all parts (subgraphs)
The Structure of Complex Networks

Ernesto Estrada

Oxford University Press

This chapter examines the concept of invariants aimed at characterising the global subgraph structure of a network. The discussions cover functions of adjacency matrix, such as the Estrada index; the global algebraic and structural properties of this index; a parameterised Estrada index and the concept of temperature in complex networks; and the statistical mechanics interpretation of this index and the development of functions that account for the entropy, total, and free energies of a network. Directed complex networks are then analysed through the use of the returnability index, which is presented using concepts of ‘chemical’ equilibrium between networks. The chapter ends with a brief account of the concepts of matrix functions used for the definition of the indices it presented earlier.

Keywords:   Estrada index, network entropy, network total energy, network free energy, network partition function, network temperature, returnability, matrix functions

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