Competition and multiscaling in evolving networks

Abstract

The rate at which nodes in a network increase their connectivity depends on their fitness to compete for links. For example, in social networks some individuals acquire more social links than others, or on the www some webpages attract considerably more links than others. We find that this competition for links translates into multiscaling, i.e. a fitness dependent dynamic exponent, allowing fitter nodes to overcome the more connected but less fit ones. Uncovering this fitter-gets-richer phenomena can help us understand in quantitative terms the evolution of many competitive systems in nature and society.PACS numbers: 5.65+b, 89. 89.75Fb, 89.75Hc. Typeset using REVT E X The complexity of many systems can be attributed to the interwoven web in which their constituents interact with each other. For example, the society is organized in a social web, whose nodes are individuals and links represent various social interactions, or the www forms a complex web whose nodes are documents and links are URLs. While for a long time these networks have been modeled as completely random [1,2], recently there is increasing evidence that they in fact have a number of generic non-random characteristics, obeying various scaling laws or displaying short length-scale clustering [3][4][5][6][7][8][9][10][11][12][13][14][15][16].A generic property of these complex systems is that they constantly evolve in time.This implies that the underlying networks are not static, but continuously change through the addition and/or removal of new nodes and links. Such evolving networks characterize the society, thanks to the birth and death of nodes and their constant acquisition of social links; or characterize the www, where the number of nodes increases exponentially and the links connecting them are constantly modified [3,6,7]. Consequently, in addressing these complex systems we have to uncover the dynamical forces that act at the level of individual nodes, whose cumulative effect determines the system's large-scale topology. A first step in this direction was the introduction of the scale-free model [8], that incorporates the fact that network evolution is driven by at least two coexisting mechanisms: (1) growth, implying that networks continuously expand by the addition of new nodes that attach to the nodes already present in the system; (2) preferential attachment, mimicking the fact that a new node links with higher probability to the nodes that already have a large number of links. With these two ingredients the scale-free model predicts the emergence of a power-law connectivity distribution, observed in many systems [3,[8][9][10], ranging from the Internet to citation networks. Furthermore, extensions of this model, including rewiring [11] or aging [12,13] have been able to account for more realistic aspects of the network evolution, such as the existence of various scaling exponents or cutoffs in the connectivity distribution.Despite its success in predicting the large-scale topology of real networks, the scalefree model neglects an ...

Generating more realistic complex networks from power-law distribution of fitness

“…The factor m is related to the fact that one new node contributes with m links to the network and the sum in the denominator is over all pre-existed nodes. The solution to equation 3 is given by [4]:…”

“…However such a model cannot to describe the topological properties of real complex networks due to some physic quantities them associated by usual exponential laws instead of power-law asymptotic behavior. Furthermore, in general real networks are more complex than Erdös and Rényi model and exhibit birth and death of nodes, aging [2], the links depending on some parameter (connectivity [3], fitness [4,5], geographic distance [6,7], etc).…”

“…A good candidate to be the other parameter is something associated to content and marketing of this document. Bianconi and Barabsi [4] associate the "good candidate" with some intrinsic quality of nodes, such as the content of a web page in the WWW, the skill in the sexual network or the knowledge in the citation network. They call this parameter the node's fitness.…”

Information cascade on networks

“…The influencers became the hubs and affected many of those involved. Hence, in this work we consider a voting model in terms of different kinds of graphs, namely random graphs, the Barabási-Albert(BA) model [18], and the fitness model [19], [20], and compare the results to determine the effect of networks.…”

Modeling for evolving biological networks with scale-free connectivity, hierarchical modularity, and disassortativity

“…It is reported that the BA and MM model have no disassortativity [27,28]. Pastor-Satorras et al [28] and Barrat et al [31] respectively argue that disassortativity emerges with competitive dynamics [32] and weight-driven dynamics [33], suggesting that growing mechanism needs to include fitness such as spatial distance [34], aging [35], and so on.…”