Effects of accelerating growth on the evolution of weighted complex networks

Abstract

Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for the evolutions and distributions for strength, degree, and weight, which are relevant to accelerating growth. We also find that accelerating growth determines the clustering coefficient of the networks. Interestingly, the distributions for strength, degree, and weight display a transition from scale-free to exponential form when the parameter with respect to accelerating growth increases from a small to large value. All the theoretical predictions are successfully contrasted with numerical simulations.

Structural Dynamics and Intentional Governance in Strategic Interorganizational Network Evolution: A Multilevel Approach

“…Second, by leveraging studies that lie at the intersection between network research and complexity science (Dorogovtsev & Mendes, 2003; Mattick & Gagen, 2005; Newman et al, 2006; Palla et al, 2007), we clarify the logics underlying the key models of network structural dynamics (Gay & Dousset, 2005). By applying these constructs we are able to posit that the network of formal ties performs according to the accelerating network model (Barabási & Albert, 1999; Zhang et al, 2009), while the network of informal ties follows the scale-free (or truncated scale-free) network model (Amaral et al, 2000). We believe that, taken together, these two contributions append a few nontrivial conceptual bricks to putting together the rudiments of a theory of network governance dynamics.…”

“…For networks whose growth is constrained the coordination and integration required to support network functionality and expansion makes the total number of ties between nodes scale faster than linearly with node number (Dorogovtsev & Mendes, 2001, 2003; Mattick & Gagen, 2005; Palla et al, 2007; Zhang, Fang, Zhou & Guan, 2009). 4 These networks are termed accelerating networks , as the connections required to sustain network expansion grow exponentially (Dorogovtsev & Mendes, 2001; Mattick & Gagen, 2005; Zhang et al, 2009) and reach a structural saturation point , beyond which the costs of integration exceed its advantages. Once an accelerating network has achieved the edge of structural saturation, it may evolve in two directions: (a) fragmentation; or (b) a change in the basis of network connections that reduce their cost.…”

Topology properties of a weighted multi-local-world evolving network

“…Tong and Zhang [16] proposed a weighted group preferential model wherein all of its distributions follow a power-law distribution. Zhang and Fang [17] proposed a weighted model with accelerating growth wherein their distributions of degree, weight and strength are subject to a transition from a power-law to an exponential shape. Rui and Ban [18] proposed a nonlinear growth in weighted networks with neighborhood preferential attachment and obtained a wide-range power-law distribution for node degree, strength, and weight.…”

Influence of the nearest-neighbor connections on shaping weighted evolving network

“…It displays scale-free behaviors for the distributions of node degree, strength and edge weight. Many extended models were later designed by adding new evolution rules including traffic-driven growth [17], spatial constraints [18], group-based preferential attachment [19] and accelerating growth [20][21][22].…”