Abstract
Emerging behaviour of a network is a consequence of the network’s structure. However, it may often not be easy to find out how this relation between structure and behaviour exactly is. In this chapter, results are presented on how certain properties of network structure determine network behaviour. The network structure characteristics considered include both connectivity characteristics in terms of being strongly connected, and aggregation characteristics in terms of properties of combination functions to aggregate multiple impacts on a state. In particular, results are found for networks that are strongly connected and combination functions that are strictly monotonically increasing and scalar-free. This class of combination functions includes linear combination functions such as scaled sum functions but also nonlinear ones such as Euclidean combination functions of any order n and scaled geometric mean combination functions. In addition, some results are found on how timing characteristics affect final outcomes of the network behaviour.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bosse, T., Duell, R., Memon, Z.A., Treur, J., van der Wal, C.N.: Agent-based modeling of emotion contagion in groups. Cogn. Comput. 7, 111–136 (2015)
Brauer, F., Nohel, J.A.: Qualitative Theory of Ordinary Differential Equations. Benjamin (1969)
Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)
Hendrickx, J.M., Tsitsiklis, J.N.: Convergence of type-symmetric and cut-balanced consensus seeking systems. IEEE Trans. Autom. Control 58(1), 214–218. (2013) Extended version: ar**v:1102.2361v2[cs.SY]
Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins Co. (1924), 2nd ed. Dover Publications (1956)
Pearl, J.: Causality. Cambridge University Press, Cambridge (2000)
Picard, E.: Traité d’Analyse, vol. 1 (1891), vol. 2 (1893)
Poincaré, H.: Mémoire sur les courbes défine par une équation différentielle (On curves defined by differential equations) (1881–1882) (1881)
Treur, J.: Verification of temporal-causal network models by mathematical analysis. Vietnam J. Comput. Sci. 3, 207–221 (2016a)
Treur, J.: Network-Oriented Modeling: Addressing Complexity of Cognitive, Affective and Social Interactions. Springer Publishers (2016b)
Treur, J.: Modelling and analysis of the dynamics of adaptive temporal-causal network models for evolving social interactions. Comput. Soc. Netw. 4, article 4, 1–20 (2017)
Treur, J.: Relating emerging network behaviour to network structure. In: Proceedings of the 7th International Conference on Complex Networks and their Applications, Complex Networks’ 18, vol. 1. Studies in Computational Intelligence, vol. 812, pp. 619–634. Springer Publishers (2018a)
Treur, J.: Mathematical analysis of a network’s asymptotic behaviour based on its strongly connected components. In: Proceedings of the 7th International Conference on Complex Networks and their Applications, Complex Networks’ 18, vol. 1. Studies in Computational Intelligence, vol. 812, pp. 663–679. Springer Publishers (2018b)
Treur, J.: Relating an adaptive social network’s structure to its emerging behaviour based on homophily. In: Proceedings of the 7th International Conference on Complex Networks and their Applications, Complex Networks’ 18. Springer, vol. 2. Studies in Computational Intelligence, vol. 813, pp. 341–356. Springer Publishers (2018c)
Treur, J.: Relating an adaptive network’s structure to its emerging behaviour for Hebbian learning. In: Martín-Vide, C., Vega-Rodríguez, M.A., Fagan, D., O’Neill, M. (eds.), Theory and Practice of Natural Computing: 7th International Conference, TPNC 2018. Lecture Notes in Computer Science, vol. 11324, pp. 359–373. Springer Publishers (2018d)
Treur, J.: The ins and outs of network-oriented modeling: from biological networks and mental networks to social networks and beyond. Trans. Comput. Collective Intell. 32, 120–139. Keynote Lecture at ICCCI’18 (2019)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Treur, J. (2020). Relating Emerging Network Behaviour to Network Structure. In: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Studies in Systems, Decision and Control, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-030-31445-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-31445-3_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31444-6
Online ISBN: 978-3-030-31445-3
eBook Packages: EngineeringEngineering (R0)