Self-organized network evolution coupled to extremal dynamics

Garlaschelli, Diego; Capocci, Andrea; Caldarelli, Guido

doi:10.1038/nphys729

Cited by 96 publications

(75 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different mechanisms may be contributing simultaneously to the evolution of a real-world complex network. The present paper suggested that the interplay between dynamics and structure can be an important driving force for the formation and stabilization of heterogeneous structures which are ubiquitous in biological and social systems [8,10,11,13,14,16,17,18,19]. A lot of efforts are needed to decipher the detailed dynamics-structure coupling mechanisms in many complex systems.…”

Section: Discussionmentioning

confidence: 99%

“…The system only needs to accumulate decentralized and local structural changes under the selection of dynamics-structure coupling. Networks with pronounced power-law degree distributions also emerged in other model systems with comparable dynamicl and evolutionary time scales [16,17]. In real-world systems, it was noticed by Aldana [26] that a major fraction of scale-free complex networks has their decay exponent γ in the tiny range of γ ∈ [2.0, 2.5].…”

Section: Dynamics and Evolutionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics-driven evolution to structural heterogeneity in complex networks

Shao

Zhou

2009

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local mutations have higher chances of getting integrated into its structure, the system can evolve into a highly heterogeneous small-world with a global hub (whose connectivity is proportional to the network size), strong local connection correlations and power law-like degree distribution. Networks with better dynamical performance are achieved if structural evolution occurs much slower than the network dynamics. Structural heterogeneity of many biological and social dynamical systems may also be driven by various dynamics-structure coupling mechanisms.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Dynamics and Evolutionmentioning

confidence: 99%

Dynamics-driven evolution to structural heterogeneity in complex networks

Shao

Zhou

2009

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Being so well studied, the Bak-Sneppen model is ideal for studying the effects introduced by a feedback mechanism between fitness dynamics and topological restructuring. For this reason, it is at the basis of the adaptive model [6] that we shall present in detail in section 4.…”

Section: The Bak-sneppen Modelmentioning

confidence: 99%

“…In particular, we shall present a self-organized model [6] where an otherwise static model of network formation driven by vertex fitness [7] is explicitly coupled to an extremal dynamics process [8] providing an evolution rule for the fitness itself. In order to highlight the novel phenomena that originate from the interplay between the two mechanisms, we first review the main properties of the latter when considered separately.…”

Section: Introductionmentioning

confidence: 99%

Self-Organization and Complex Networks

Caldarelli¹,

Garlaschelli

2009

Understanding Complex Systems

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…ITN is defined as the network of import-export relationships between world countries in a given period (usually a year). Many efforts have been devoted to analyze the structure and the dynamics of the ITN from an empirical and theoretical modeling perspective (see, for instance, [18][19][20][21][22][23][24][25][26]). In particular, since it is a dense weighted network, it is rather difficult to define a tractable reference case against which one can measure the specific features of the real system.…”

mentioning

confidence: 99%

Weighted networks as randomly reinforced urn processes

et al. 2013

Self Cite

View full text Add to dashboard Cite

We analyze weighted networks as randomly reinforced urn processes, in which the edge-total weights are determined by a reinforcement mechanism. We develop a statistical test and a procedure based on it to study the evolution of networks over time, detecting the "dominance" of some edges with respect to the others and then assessing if a given instance of the network is taken at its steady state or not. Distance from the steady state can be considered as a measure of the relevance of the observed properties of the network. Our results are quite general, in the sense that they are not based on a particular probability distribution or functional form of the random weights. Moreover, the proposed tool can be applied also to dense networks, which have received little attention by the network community so far, since they are often problematic. We apply our procedure in the context of the International Trade Network, determining a core of "dominant edges. [10], and others, which can be efficiently described by a network structure, where the nodes are the system entities and the edges represent the relations between them. All the models that produce complex networks are based either on preferential attachment (or copying mechanism) or on a fitness (hidden variables) microscopic mechanism. Unfortunately, no statistical method has been developed in order to assess the relevance of both experimental data and model simulations. In this paper, we present a model of network evolution based on randomly reinforced urn (RRU) processes [11][12][13][14]. In our model we map the weight associated to a given edge with the number of balls of a given color, which are added in an urn so that at a given time step the probability of picking an edge (color) depends on the total weight associated with it until that time. At each time step we first extract an edge (color) with probability proportional to its total weight and then we associate to it a random weight (number of added balls) which increases its total weight. This results in a preferential attachment (PA) rule for edges with random weights. Hence, although our model can be considered as a particular refinement in the class of the PA mechanisms, its novelty is in the connection that we can establish between complex networks and RRU models [15]. RRU theory allows us to develop a procedure for the detection of the "dominant edges" in the evolution of a weighted network and for an evaluation of the distance from the steady state of the network, in the sense that we can assess if the structure observed at a given time is what we can expect at the steady state or not. The novelty of our methodology is also related to its applicability to dense, weighted networks (a situation often problematic both for modeling and for randomization) [16].We consider a system with N vertices and Lpotential edges (directed or not). Hereafter we indicate the various edges by the index (with ∈ [1,L]). Our model defines a weighted adjacency matrix W t for every time step t, where the generic element w t =...

show abstract

Self-organized network evolution coupled to extremal dynamics

Cited by 96 publications

References 29 publications

Dynamics-driven evolution to structural heterogeneity in complex networks

Dynamics-driven evolution to structural heterogeneity in complex networks

Self-Organization and Complex Networks

Weighted networks as randomly reinforced urn processes

Contact Info

Product

Resources

About