On dynamic random graphs with degree homogenization via anti-preferential attachment probabilities

Abstract

We analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using, with probability $p$, an anti-preferential attachment mechanism or, with probability $1-p$, a preferential attachment mechanism. We derive the asymptotic degree distribution in the general case and study the asymptotic behaviour of the expected degree process in the general and that of the degree process in the pure anti-preferential attachment case. Degree homogenization mainly affects convergence rates for the former case and also the limiting degree distribution in the latter.

References in corpus (16)

• Emergence of scaling in random networks
• The structure and function of complex networks
• Assortative mixing in networks
• Connectivity of Growing Random Networks
• Scale-free networks are rare
• Organization of Growing Random Networks
• Emergence of assortative mixing between clusters of cultured neurons
• Random networks with sublinear preferential attachment: The giant component
• Emergence of small-world anatomical networks in self-organizing clustered neuronal cultures
• On a preferential attachment and generalized Pólya's urn model
• Scale-free behavior of networks with the copresence of preferential and uniform attachment rules
• Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks
• Preferential attachment with choice
• A dynamic network in a dynamic population: asymptotic properties
• The role of detachment of in-links in scale-free networks
• Deletion of oldest edges in a preferential attachment graph

Cited by in corpus (1)

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