Network evolution and the emergence of structure
type: Item
instance of: scholarly article
zbMATH Open document ID: 0978.93005
author: D. A. Seeley
publication date: 2002-01-27T00:00:00Z
Mathematics Subject Classification ID: 93A10
Mathematics Subject Classification ID: 90B15
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 1578060
zbMATH Keywords: graph
zbMATH Keywords: macroscopic quantities
zbMATH Keywords: complex systems
zbMATH Keywords: networks
zbMATH Keywords: cycles
zbMATH Keywords: trees
zbMATH Keywords: connectivity
zbMATH Keywords: fractals
zbMATH Keywords: phase transitions
zbMATH Keywords: self-organization
zbMATH Keywords: bifurcation
zbMATH Keywords: critical situation
MaRDI profile type: Publication
title: Network evolution and the emergence of structure
review text: This publication defends the point of view according to which depending on the number of connections in a graph, entities may appear and these could be seen as modeling macroscopic quantities in complex systems.NEWLINENEWLINENEWLINEAn introduction illustrates that networks permeate our world.NEWLINENEWLINENEWLINEA first section settles the terminology (graphs, networks, cycles, trees) and states that graphs can be extracted from various types of models (matrix for linear ODEs, Markov processes, automata); the structure of the dependency graph (cycles, trees) influences the behaviour in state space and conversely, in the case of automata, cyclic trajectories may help classify the running system.NEWLINENEWLINENEWLINEA second section describes the qualitative behaviours which occur in a digraph when one adds connections (randomly). The main feature is the appearance of a sharp increase in connectivity after having added some connections (little less than half the number of nodes). A giant component is formed and various embedded cyclic structures manifest themselves afterwards until full connectedness is obtained. Then the author tries to illustrate that this type of ``phase change'' has analogs in various situations with abrupt change leading to ergodic type behaviour (cf. cellular automata which may be self-reproducing in suitable circumstances).NEWLINENEWLINENEWLINEAnother section presents a ``local point of view'' in the sense that one looks at the nodes connected to a particular one and circuits and forking structures are formed, duplicated, absorbed in a self-similar fashion which is reminiscent to the internal structure of fractals.NEWLINENEWLINENEWLINEFinally, the author considers examples (physiological, psychological, sociological, ecological, technological, management, computational).NEWLINENEWLINENEWLINEIn the conclusion, the author stresses that structural changes due to phase transitions, the birth of chaos and self-organization can have a paradigmatic ex…
reviewed by: A. Akutowicz
description: scientific article