Self-Organization and Complex Networks

Abstract

In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation selfcontained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.

Analysis of Social Network Dynamics with Models from the Theory of Complex Adaptive Systems

“…to the complexity realm. Th the predictions and actions these actions as the system ractions difficult to decomp opinion formation process, and the evolution of the to nd G. Lekakos e opposite, that is the effect of node-specific dynam ture [17]. As a result an interesting line of research is ned effect of these processes on each other.…”

“…Nevertheless, when trying to reproduce the topological properties of real networks by means of simple graph models there exist difficulties in deriving certain properties often common between networks of different nature thus indicating the existence of common organizing mechanisms [17]. The limitations -inherent in simple graph models-have been the subject of recent research focusing on the temporal aspects of networks growth as well as on the dynamics occurring on local and global level.…”

“…Since the social network evolution is based on the co-evolutionary adaptation of dynamics and topology by local rewiring rules, a question emanating from this observation is whether co-evolution of dynamics extends to a global time scale despite the local nature of the rewiring events and a significant time scale separation between dynamical and topological updates [28]. Focusing on the interactions between the nodes of a social network rather than the attributes of the nodes themselves for deriving insights as to the dynamics taking place on social networks, an interdisciplinary perspective is being formed encompassing the scientific fields of statistical physics, nonlinear dynamics, critical phenomena, fractal geometry, spin glasses, and many-body theory [17].…”

“…In general, the main fields of social network research concern: (i) the study of the static topological properties, (ii) the modeling of network formation (either static or growing), and (iii) how the dynamical processes occurring on networks are affected by the network topology [17].…”

“…The Hebbian learning shows that network self-organization by correlation-driven rewiring is robust even when spatial constraints are present and dynamics is affected by noise [34]. The phenomenon of self organized criticality constitutes an important feature of adaptive networks and boils down to the fact that each node in a network is recipient of dynamical information which relates to the connectivity of the entire network, thereby providing global information to individual nodes thus causing the network to organize itself [17,28].…”