Dynamics-driven evolution to structural heterogeneity in complex networks

Shao, Zongshu; Zhou, Haijun

doi:10.1016/j.physa.2008.10.024

Cited by 9 publications

(8 citation statements)

References 24 publications

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“…A deeper understanding of this mutual relation between structure and dynamics can be achieved either by studying empirical systems directly, in a biological context for instance physiological networks [7], food webs [8], or protein interaction networks [9], or by modeling of network evolution towards a desired dynamical performance and in this way gain new insight into many empirical networks. Concerning the latter, the evolution of dynamical networks was previously applied in the contexts of modularity in changing environments [10], Boolean (threshold) dynamics [11][12][13][14][15][16], and synchronization of oscillatory systems [17][18][19][20][21]. It is known that the dynamical behavior is closely related to the network's spectral properties [22], which was exploited in studies in which the Laplacian eigenratio [23] was maximized by network evolution [17][18][19][20].…”

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confidence: 99%

Network evolution towards optimal dynamical performance

Karalus¹,

Porto²

2012

EPL

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Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this relationship which is applicable to a wide class of dynamics, namely to evolve networks using a performance measure based on the whole spectrum of the dynamics' time evolution operator. As an example, we consider the graph Laplacian describing diffusion processes, and we evolve the network structure such that a given sub-diffusive behavior emerges.

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confidence: 99%

Network evolution towards optimal dynamical performance

Karalus¹,

Porto²

2012

EPL

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“…here ∂i means the vertices which are connected with vertex i directly. As described in [18], we start a LMR dynamical process from a strongly disordered configuration σ(0) ≡ {σ 1 (0), σ 2 (0), . .…”

Section: A Local-majority-rule Dynamicsmentioning

confidence: 99%

“…Obviously, this compositional difference indicates an apparent optimization achieved by evaluation-driven evolution. Thus, if we take the dynamics-driven evolution as particles jumping among a series of structural heterogeneity levels, it could be easily derived from above analysis that the optimal structure could be approached only when the timescale of mutations is much longer than that of dynamical processes [18].…”

Section: Introductionmentioning

confidence: 99%

Evolve Networks Towards Better Performance: a Compromise between Mutation and Selection

Shao,

Zhou

2009

Preprint

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The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue by a simple model system, in which the topological structure of networks is repeatedly modified and selected in order to make them have better performance in dynamical processes. Interestingly, when the networks with optimal performance deviate from the steady state networks under pure mutations, we find the evolution behaves as a balance between mutation and selection. Furthermore, when the timescales of mutations and dynamical processes are comparable with each other, the steady state of evolution is mainly determined by mutation. On the opposite side, when the timescale of mutations is much longer than that of dynamical processes, selection dominates the evolution and the steady-state networks turn to have much improved performance and highly heterogeneous structures. Despite the simplicity of our model system, this finding could give useful indication to detect the underlying mechanisms that rein the evolution of real systems.

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“…The emerging global effects of protocols based on local interactions are studied in the distributed algorithms field. For instance, the interplay between the election/consensus problems and the protocols based on majority rules has been extensively studied in several works such as [22] [26], [33], [6], [32] and [16]. In fact, social behaviors often provide useful insights in determining the way problems are solved in computer science.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Monopolies in Colored Tori

Brunetti

Lodi

2011

2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and PHD Forum

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The {\em information diffusion} has been modeled as the spread of an information within a group through a process of social influence, where the diffusion is driven by the so called {\em influential network}. Such a process, which has been intensively studied under the name of {\em viral marketing}, has the goal to select an initial good set of individuals that will promote a new idea (or message) by spreading the "rumor" within the entire social network through the word-of-mouth.\ud Several studies used the {\em linear threshold model} where the group is represented by a graph, nodes have two possible states (active, non-active), and the threshold triggering the adoption (activation) of a new idea to a node is given by the number of the active neighbors.\ud \ud The problem of detecting in a graph the presence of the minimal number of nodes that will be able to activate the entire network is called {\em target set selection} (TSS). In this paper we extend TSS by allowing nodes to have more than two colors.\ud The multicolored version of the TSS can be described as follows: let $G$ be a torus where every node is assigned a color from a finite set of colors. At each local time step, each node can recolor itself, depending on the local configurations, with the color held by the majority of its neighbors.\ud \ud We study the initial distributions of colors leading the system to a monochromatic configuration of color $k$, focusing on the minimum number of initial $k$-colored nodes. We conclude the paper by providing the time complexity to achieve the monochromatic configuration

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Dynamics-driven evolution to structural heterogeneity in complex networks

Cited by 9 publications

References 24 publications

Network evolution towards optimal dynamical performance

Network evolution towards optimal dynamical performance

Evolve Networks Towards Better Performance: a Compromise between Mutation and Selection

Dynamic Monopolies in Colored Tori

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