Abstract
We propose a growing network model that can generate dense scale-free networks with an almost neutral degree−degree correlation and a negative scaling of local clustering coefficient. The model is obtained by modifying an existing model in the literature that can also generate dense scale-free networks but with a different higher-order network structure. The modification is mediated by category theory. Category theory can identify a duality structure hidden in the previous model. The proposed model is built so that the identified duality is preserved. This work is a novel application of category theory for designing a network model focusing on a universal algebraic structure.
Highlights
Recall that the algorithm of the BA model consists of two steps: growth and preferential attachment (PA)[3]
We show that the generated networks have an almost neutral degree−degree correlation and a negative scaling of local clustering coefficient
Note that the converse implication holds for δ ≥ 1, which corresponds to the dense regime of interest in this paper
Summary
Recall that the algorithm of the BA model consists of two steps: growth and preferential attachment (PA)[3]. A new node enters into an existing network. In the PA step, each existing node acquires a new link to the new node with probability proportional to its degree. A new node is produced by copying a randomly chosen existing node together with links emanating from it. Each link from the new node is deleted with a given probability 0 < p < 1. PA follows from the copying step because the higher the degree of a node is, the higher the probability that it is reached from a randomly chosen node is. It is known that the generated networks by the copying model have a powerlaw degree distribution pk ∼ k−γ with 2 ≤ γ ≤ 3 when p ≤ 12 , and they are dense but not scale-free for p > 1212
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