Effects of Fitness on Generative Graph Models with Preferential Attachment

Preferential Attachment models offer an explanation for why power laws are so common in real-world data. In these models, we start out with an initial network and add nodes one at a time. For each new node, we make m connections to existing nodes and if we define the attachment probability of attaching to a vertex to be proportional to its...

Dynamical fitness models: evidence of universality classes for preferential attachment graphs

In this paper we define a family of preferential attachment models for random graphs with fitness in the following way: independently for each node, at each time step a random fitness is drawn according to the position of a moving average process with positive increments. We will define two regimes in which our graph reproduces some features...

Self-organizing topology for energy-efficient ad-hoc communication networks of mobile devices

When physical communication network infrastructures fail, infrastructure-less communication networks such as mobile ad-hoc networks (MANET), can provide an alternative. This, however, requires MANETs to be adaptable to dynamic contexts characterized by the changing density and mobility of devices and availability of energy sources. To address...

A Social Network Model Exhibiting Tunable Overlapping Community Structure

Social networks, as well as many other real-world networks, exhibit overlapping community structure. In this paper, we present formulas which facilitate the computation for characterizing the overlapping community structure of networks. A hypergraph representation of networks with overlapping community structure is introduced. Using the...

Diameters in preferential attachment models

In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional to the degree plus a constant, i.e., we consider affine PA-models. There is a substantial amount of...

The Strength of Preference

Growth and preferential attachment are the two ingredients of the scale-free network. Based on the Barabási-Albert scale-free model, we construct a more general model by replacing the linear preferential attachment with the nonlinear preferential attachment. We introduce different networks by controlling a parameter ? which decides the...

Random graphs: From static to dynamic

Many empirical studies on real-life networks show that many networks are small worlds, meaning that typical distances in these networks are small, and many of them have power-law degree sequences, meaning that the number of nodes with degree k falls off as kˆ (-τ) for some exponent τ>1. These networks are modeled by means of scale-free random...