Analysis of a Network’s Asymptotic Behaviour via its Structure Involving its Strongly Connected Components

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Abstract

In this paper it is addressed how network structure can be related to asymptotic network behaviour. If such a relation is studied, that usually concerns only strongly connected networks and only linear func-tions describing the dynamics. In this paper both conditions are generalised. A couple of general theo-rems is presented that relates asymptotic behaviour of a network to the network’s structure characteris-tics. The network structure characteristics on the one hand concern the network’s strongly connected components and their mutual connections; this generalises the condition of being strongly connected to a very general condition. On the other hand the network structure characteristics considered generalise from linear functions to functions that are normalised, monotonic and scalar-free, so that many nonlinear functions are also covered. Thus the contributed theorems generalise existing theorems on the relation between network structure and asymptotic network behaviour only addressing specific cases such as acyclic networks, fully and strongly connected networks, and theorems addressing only linear func-tions.
Original languageEnglish
JournalNetwork Science
Publication statusPublished - 1 Oct 2019

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general conditions

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title = "Analysis of a Network’s Asymptotic Behaviour via its Structure Involving its Strongly Connected Components",
abstract = "In this paper it is addressed how network structure can be related to asymptotic network behaviour. If such a relation is studied, that usually concerns only strongly connected networks and only linear func-tions describing the dynamics. In this paper both conditions are generalised. A couple of general theo-rems is presented that relates asymptotic behaviour of a network to the network’s structure characteris-tics. The network structure characteristics on the one hand concern the network’s strongly connected components and their mutual connections; this generalises the condition of being strongly connected to a very general condition. On the other hand the network structure characteristics considered generalise from linear functions to functions that are normalised, monotonic and scalar-free, so that many nonlinear functions are also covered. Thus the contributed theorems generalise existing theorems on the relation between network structure and asymptotic network behaviour only addressing specific cases such as acyclic networks, fully and strongly connected networks, and theorems addressing only linear func-tions.",
author = "Jan Treur",
year = "2019",
month = "10",
day = "1",
language = "English",
journal = "Network Science",
issn = "2050-1242",
publisher = "Cambridge University Press",

}

Analysis of a Network’s Asymptotic Behaviour via its Structure Involving its Strongly Connected Components. / Treur, Jan.

In: Network Science, 01.10.2019.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

T1 - Analysis of a Network’s Asymptotic Behaviour via its Structure Involving its Strongly Connected Components

AU - Treur, Jan

PY - 2019/10/1

Y1 - 2019/10/1

N2 - In this paper it is addressed how network structure can be related to asymptotic network behaviour. If such a relation is studied, that usually concerns only strongly connected networks and only linear func-tions describing the dynamics. In this paper both conditions are generalised. A couple of general theo-rems is presented that relates asymptotic behaviour of a network to the network’s structure characteris-tics. The network structure characteristics on the one hand concern the network’s strongly connected components and their mutual connections; this generalises the condition of being strongly connected to a very general condition. On the other hand the network structure characteristics considered generalise from linear functions to functions that are normalised, monotonic and scalar-free, so that many nonlinear functions are also covered. Thus the contributed theorems generalise existing theorems on the relation between network structure and asymptotic network behaviour only addressing specific cases such as acyclic networks, fully and strongly connected networks, and theorems addressing only linear func-tions.

AB - In this paper it is addressed how network structure can be related to asymptotic network behaviour. If such a relation is studied, that usually concerns only strongly connected networks and only linear func-tions describing the dynamics. In this paper both conditions are generalised. A couple of general theo-rems is presented that relates asymptotic behaviour of a network to the network’s structure characteris-tics. The network structure characteristics on the one hand concern the network’s strongly connected components and their mutual connections; this generalises the condition of being strongly connected to a very general condition. On the other hand the network structure characteristics considered generalise from linear functions to functions that are normalised, monotonic and scalar-free, so that many nonlinear functions are also covered. Thus the contributed theorems generalise existing theorems on the relation between network structure and asymptotic network behaviour only addressing specific cases such as acyclic networks, fully and strongly connected networks, and theorems addressing only linear func-tions.

M3 - Article

JO - Network Science

JF - Network Science

SN - 2050-1242

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