Emergence of dense scale-free networks and simplicial complexes by random degree-copying

Abstract

Many real-world networks exhibit dense and scale-free properties, that is, the amount of connections among the nodes is large and the degree distribution follows a power-law P(k)∼k−γ. In particular, for dense networks γ∈(1,2]. In the literature, numerous network growth models have been proposed with the aim to reproduce structural properties of these networks. However, most of them are not capable of generating dense networks and power-laws with exponents in the correct range of values. In this research, we provide a new network growth model that enables the construction of networks with degree distributions following a power law with exponents ranging from one to an arbitrary large number. In our model, the growth of the network is made using the well-known Barabási–Albert model, that is, by nodes and links addition and preferential attachment. The amount of connections with which each node is born, can be fixed or depending of the network structure incorporating a random degree-copying mechanism. Our results indicate that if degree-copying mechanism is applied most of the time, then the resulting degree distribution has an exponent tending to one. Also, we show that the resulting networks become denser as γ→1, in consequence their clustering coefficient increases and network diameter decreases. In addition, we study the emergence of simplicial complexes on the resulting networks, finding that largest simplicial dimension appears as γ decreases.