Linear processes on complex networks

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Abstract

This article studies the dynamics of complex networks with a time-invariant underlying topology, composed of nodes with linear internal dynamics and linear dynamic interactions between them. While graph theory defines the underlying topology of a network, a linear time-invariant state-space model analytically describes the internal dynamics of each node in the network. By combining linear systems theory and graph theory, we provide an explicit analytical solution for the network dynamics in discrete-time, continuous-time and the Laplace domain. The proposed theoretical framework is scalable and allows hierarchical structuring of complex networks with linear processes while preserving the information about network, which makes the approach reversible and applicable to large-scale networks.

Original languageEnglish
Pages (from-to)1-41
Number of pages41
JournalJournal of Complex Networks
Volume8
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Complex networks
  • Large-scale networks
  • Linear dynamics
  • Linear interactions
  • Network dynamics

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