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 Barabasi-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
Erdos collaboration network of mathematicians.
