Vertex intrinsic fitness: How to produce arbitrary scale-free networks

Abstract

We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved. We study here different choices for the probability distribution densities and the linking functions. We find that, irrespective of the particular choices, the generation of scale-free networks is straightforward. We then derive the general conditions under which scale-free behavior appears. This model could then represent a possible explanation for the ubiquity and robustness of such structures.

A microscopic study of the fitness-dependent topology of the world trade network

“…However, the averages do not represent good approximations for the bins, the data in the bins is distributed over a wide range of k. The original derivation of various topological properties in Ref. [2] uses the fact that E[k|x] is invertible. That implies that the distribution of k inside the bins must be relatively narrow.…”

“…[1,28,2]. The investigation that is presented later in the text relies on results that are reviewed in the following.…”

“…A detailed understanding of the network structure of international trade facilitates a better comprehension of crises that spread across a country's frontiers. It is generally agreed that a static hidden variable model [1,2] best describes the topology of the WTN. The static model is most suitable because there are only a finite number of distinct countries in the world.…”

Fitness-based network growth with dynamic feedback

“…Both the distribution of fitnesses and the connection rules are given by a priori arbitrary functions, thus allowing a considerable amount of tuning in such models. This feature enables fitness-based models to mimic a variety of network topologies, in particular, subject to some constraints, they can be tuned to reproduce a given type of degree distributions and even degree correlation functions [4,5,7]. This tunability makes fitness-based models useful as a modeling tool, but also imparts a degree of arbitrariness which makes them less attractive as a robust explanation for the universality of naturally observed behaviors.…”

“…Such considerations provided one of the motivations for the study of a different class of growth mechanisms, variously known as hidden variable or fitness-based models [4][5][6][7]. The models of this type are characterized by probabilistic rules for forming connections between nodes based on a static measure of intrinsic node attractiveness, usually termed fitness.…”