System Theory

Adaptive networks: theory, models and applications by Thilo Gross, Hiroki Sayama

By Thilo Gross, Hiroki Sayama

With adaptive, advanced networks, the evolution of the community topology and the dynamical strategies at the community are both very important and infrequently essentially entangled.

Recent learn has proven that such networks can express a plethora of recent phenomena that are eventually required to explain many real-world networks. a few of these phenomena contain powerful self-organization in the direction of dynamical criticality, formation of complicated international topologies in accordance with uncomplicated, neighborhood principles, and the spontaneous department of "labor" within which an first and foremost homogenous inhabitants of community nodes self-organizes into functionally designated sessions. those are only a couple of.

This ebook is a state of the art survey of these distinct networks. In it, major researchers got down to outline the long run scope and course of a few of the main complicated advancements within the great box of advanced community technological know-how and its applications.

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1 140 0 5 10 15 20 t 25 30 35 40 Fig. 13 (a) The average age τ of communities with a given size (number of people) s, divided by the average age of all communities τ , as the function of s, indicating that larger communities are on average older. (b) The average auto-correlation function C(t) of communities with different sizes (the unit of time, t, is one month). The C(t) of larger communities decays faster. 975 1 ζ Fig. 14 (a) The average life-span τ ∗ of the communities as the function of the stationarity ζ and the community size s for the co-authorship network.

Palla et al. a) b) phone−call co−authorship 1 1 t=0 t=5 t = 10 t = 15 10–1 P(s) 10–2 P(s) 10–3 1 c) 10–4 1 102 10 s d) phone−call 10 10–2 10–3 10–4 10–5 t=0 t = 15 t = 30 t = 60 t = 90 t = 120 10–1 10 co−authorship 4 t=0 t = 15 t = 30 t = 60 t = 90 t = 120 103 103 N(s) 10 102 s t=0 t=5 t = 10 t = 15 2 102 N(s) 10 10 1 1 1 10 s 102 1 10 s 102 Fig. 12 (a) The cumulative community size distribution in the phone-call network at different time steps. (b) The time evolution of the cumulative community size distribution in the coauthorship network.

When a node previously belonging to none of the communities joins a community, communities with large size and large degree are selected with enhanced probability from the available communities. 3 Model for Growth of Community Network In this section we outline a simple model for the growth of overlapping communities. Our goal is to demonstrate that preferential attachment of the nodes to communities with the community size, together with minor additional assumptions are enough for the emergence of a community system with a scaling community size and community degree distribution.

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