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

Abstract

In this work we analyze the implications of using a power law distribution of vertice's quality in the growth dynamics of a network studied by Bianconi and Barabási. Using this suggested distribution we show the degree distribution interpolates the Barabási et al. model and Bianconi et al. model. This modified model (with power law distribution) can help us understand the evolution of complex systems. Additionally, we determine the exponent gamma related to the degree distribution, the time evolution of the average number of links, < k i >∝ (t/i) β (i coincindes with the input-time of the i th node), the average path length and the clustering coefficient.

Investigating the Influence of Inverse Preferential Attachment on Network Development

“…First, although network scientists have previously examined the influence of constraints of costs on network growth (e.g., financial or space limitations on the expansion of air transportation networks [ 27 ]), the present findings suggest that it may also be important to consider how different costs introduced at different time-points of development shape future network growth. Second, network scientists commonly view network growth as operating via a process that maximizes node fitness [ 3 , 5 ]. In the case of preferential attachment and close variants of this model, the fitness of an individual node (i.e., its ability to gain new edges) is maximized by attaching to a high-degree node.…”

“…A common feature across diverse complex networks is their scale-free degree distribution, whereby most nodes in the network have very few edges or links and a few nodes have many edges or links. Preferential attachment models of network growth, where new nodes that are added to the network tend to connect to existing nodes with many links (i.e., high degree nodes), have been prominent in the literature covering network growth and evolution, because such models describe a generic mechanism that provides an elegant account of the emergence of scale-free complex networks [ 2 , 3 , 4 , 5 ]. In this paper, we conducted a series of network simulations to specifically examine the properties of networks grown via a different mechanism, which we refer to as inverse preferential attachment, where new nodes added to the network tend to connect to existing nodes with fewer edges.…”

Network growth models: A behavioural basis for attachment proportional to fitness

“…In order to explain late-comers acquiring links relatively quickly, a growth model has to take into account the intrinsic property of being desired as a connection by other nodes. In network science this property is called the ‘fitness’ of the node 3 4 5 7 8 9 10 29 47 51 52 . The concept of node fitness can be thought of as the amalgamation of all the attributes of a given node that contribute to its propensity to attract links.…”

“…Preferential attachment models, such as the Barabási-Albert model where attachment probabilities are proportional to target node degree, have been the most prominent among them in the past decade 2 . Recently, a number of node fitness-based attachment models 3 4 5 6 7 8 9 10 11 12 have been gaining prominence. It is noted that the concept of node fitness in this context is parallel to the concept of utility, as used in discrete choice models, where utility is a dimensionless measure of attraction which can be expressed as a function of attributes weighted by their relative importance (for further information regarding the role of utility, refer to ref.…”

CFM: A Fitness-Model-Based Topology Control Algorithm for Wireless Sensor Networks

“…Fitness model [9,10,11] was proposed by Bianconi and Barabási in 2001 [12]. Firstly, the constructing process of a fitness network is given as follows,…”