TY - CHAP

T1 - Analysis of a network’s emerging behaviour via its structure involving its strongly connected components

AU - Treur, Jan

PY - 2020/1/1

Y1 - 2020/1/1

N2 - In this chapter, it is addressed how network structure can be related to network behaviour. If such a relation is studied, that usually concerns only strongly connected networks and only linear functions describing the aggregation of multiple impacts. In this chapter both conditions are generalised. General theorems are presented that relate emerging behaviour of a network to the network’s structure characteristics. The network structure characteristics on the one hand concern network connectivity in terms of the network’s strongly connected components and their mutual connections; this generalises the condition of being strongly connected (as addressed in Chap. 11) to a very general condition. On the other hand, the network structure characteristics considered concern aggregation by generalising from linear combination functions to any combination functions that are normalised, monotonic and scalar-free, so that many nonlinear functions are also covered (which also was done in Chap. 11). Thus the contributed theorems generalise existing theorems on the relation between network structure and network behaviour that only address specific cases (such as acyclic networks, fully and strongly connected networks, and theorems addressing only linear functions).

AB - In this chapter, it is addressed how network structure can be related to network behaviour. If such a relation is studied, that usually concerns only strongly connected networks and only linear functions describing the aggregation of multiple impacts. In this chapter both conditions are generalised. General theorems are presented that relate emerging behaviour of a network to the network’s structure characteristics. The network structure characteristics on the one hand concern network connectivity in terms of the network’s strongly connected components and their mutual connections; this generalises the condition of being strongly connected (as addressed in Chap. 11) to a very general condition. On the other hand, the network structure characteristics considered concern aggregation by generalising from linear combination functions to any combination functions that are normalised, monotonic and scalar-free, so that many nonlinear functions are also covered (which also was done in Chap. 11). Thus the contributed theorems generalise existing theorems on the relation between network structure and network behaviour that only address specific cases (such as acyclic networks, fully and strongly connected networks, and theorems addressing only linear functions).

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UR - http://www.scopus.com/inward/citedby.url?scp=85075187907&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-31445-3_12

DO - 10.1007/978-3-030-31445-3_12

M3 - Chapter

AN - SCOPUS:85075187907

SN - 9783030314446

SN - 9783030314477

T3 - Studies in Systems, Decision and Control

SP - 281

EP - 318

BT - Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models

A2 - Treur, Jan

PB - Springer International Publishing AG

ER -