Network-based models in Control

Investigation of dependencies and distributions in random networks evolved by mixed models of the evolution and node deletion

N. M. Markovich, M. S. Ryzhov, i. Kulik

V.A. Trapeznikov Institute of Control Sciences of RAS, Moscow

Abstract: The evolution of a random network by models of preferential, clustering and mixed attachments to form links between newly appending nodes and existing nodes is studied. Strategies of node deletion at each step of network evolution are considered: 1) without node and edge deletion; 2) deletion the least influential node among the most 'old', where the node's PageRank is used as a measure of the node's influence; 3) deletion a node with a probability inversely proportional to the node degree. For these deletion strategies the dependence of two characteristics of random networks, namely, the node degrees and node triangle counts (that is, the triples of interconnected nodes in which the node is involved), and the behavior of clustering coefficients of nodes are compared by simulation. The heaviness of the distribution tails for the node degrees and the node triangle counts is estimated. The mixed clustering-preferential attachment is proposed here for the first time.

Keywords: network evolution, preferential and clustering attachment, mixed clustering-preferential attachment, node degree, triangle counts, node deletion, clustering coefficient.

UDC: 519.24; 519.25
BBK: 22.172

Received: February 6, 2024
Published: May 31, 2024

DOI: 10.25728/ubs.2024.109.5