Constructing Scale-Free Networks With a Given Cluster Coefficient

Abstract

We introduce a new generation rule for local thresholding in scale-free networks based on the nodes' degree. The resulting networks are disassortative with a hierarchical structure. There is, however, a subnet of the nodes, which we call the active nodes, which is neither disassortative nor has such a structure. It is shown that networks with a wide range of cluster coefficients, ranging from very small to close to unity and with scaling exponent from 2.5 to 4 are generated by the new method, which mimic some important real-world networks.

Effect of primary cores in continuous and discontinuous percolation transition of random graph

“…[12][13][14] Another factor during the creation of a network is initial conditions that affect growth and dynamics in network. Hub connecting may have serious results in network's growth and dynamics depending on such mechanisms where the overall connectivity of a network changes qualitatively.…”

“…For instance, spontaneous activity in developing neural circuits may become continuous after increasing the number of synaptic links above a threshold. [12][13][14] Another factor during the creation of a network is initial conditions that affect growth and dynamics in network. 15,16 In this paper, we consider primary cores as initial conditions.…”