A Grid-based Model for Generating Scale-Free Networks

Amit Kumar Verma, Nikhil Prakash

Abstract: It has been observed that the evolution of complex networks such as social networks is not a random process, there exist some key features which are responsible for their evolution. One such feature is the degree distribution of these networks which follow the power law i.e. P(k) ∝ k -γ where γ is a parameter whose value is typically in the range 2 <; γ <; 3 and such networks are called scale-free networks [4]. In this paper, we formulate a model for generating scale-free networks based on Baraba̅si-Albert model [6], using insights from elementary Euclidean Geometry that takes into account the geometrical location of the nodes instead of their degrees for new connections. We show that our model generates scale-free networks experimentally and provide a mathematical proof for the correctness of the fact that the degree distribution in generated networks indeed follows the power law. We also validate our model on Erdös collaboration network of mathematicians.