Avalanche-size distribution of Cayley tree
Amikam Patron (Department of Mathematics, Jerusalem College of, Technology, Jerusalem, Israel)

TL;DR
This paper analyzes the distribution of avalanche sizes caused by single node removals in Cayley trees, providing an analytical understanding of network fragmentation during targeted attacks from a micro perspective.
Contribution
It introduces an analytical method to study avalanche size distributions in Cayley trees, focusing on micro-level node removal effects during network attacks.
Findings
Derived the analytical distribution of avalanche sizes in Cayley trees.
Showed how single node removals can cause cascading disconnections.
Provided insights into network immunization strategies.
Abstract
Attacks on networks is a very important issue in developing strategies of eradicating spreads of malicious phenomena in networks, such as epidemics and fake information, which are generally named in the research networks immunization. The traditional approach of evaluating the effectiveness of attacks on networks, is focused on measuring some macro parameters related to an entire attack, such as the critical probability of a percolation occurrence in the network and the relative size of the largest component in the network - the giant component, but not considering the attack on a micro perspective, which is the analysis of the node removals, during an attack, themselves, their characteristics and results. In this paper we present and apply the last method of focusing on the micro scale of an attack. Based on the theory of percolation in networks, we analyze the phenomenon of an…
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Taxonomy
TopicsComplex Network Analysis Techniques · Opinion Dynamics and Social Influence · Stochastic processes and statistical mechanics
