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Analysis of a network’s asymptotic behavior via its structure involving its strongly connected components

Published online by Cambridge University Press:  01 October 2019

Jan Treur Open the ORCID record for Jan Treur [Opens in a new window]
Jan Treur*
Affiliation:
Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, the Netherlands
*
Corresponding author. Email: [email protected]
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Abstract

In this paper, it is addressed how network structure can be related to asymptotic network behavior. If such a relation is studied, that usually concerns only strongly connected networks and only linear functions describing the dynamics. In this paper, both conditions are generalized. A couple of general theorems is presented that relates asymptotic behavior of a network to the network’s structure characteristics. The network structure characteristics, on the one hand, concern the network’s strongly connected components and their mutual connections; this generalizes the condition of being strongly connected to a very general condition. On the other hand, the network structure characteristics considered generalize from linear functions to functions that are normalized, monotonic, and scalar-free, so that many nonlinear functions are also covered. Thus, the contributed theorems generalize the existing theorems on the relation between network structure and asymptotic network behavior addressing only specific cases such as acyclic networks, fully, and strongly connected networks, and theorems addressing only linear functions. This paper was invited as an extended (by more than 45%) version of a Complex Networks’18 conference paper. In the discussion section, the differences are explained in more detail.

Keywords

Hocine CherifiLuis RochaStanley Wassermanasymptotic network behaviorstrongly connected componentsrelating network structure and network behavior
Type
Research Article
Information
Network Science , Volume 8 , Issue S1: Complex Networks 2018 , July 2020 , pp. S82 - S109
Copyright
© Cambridge University Press 2019

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