Analytical solution to the k-core pruning process
Physica A: Statistical Mechanics and its Applications(2022)
Abstract
k-core decomposition is a widely-used method in ranking nodes or extracting important information of complex networks. It is a pruning process in which we recursively remove the vertices with degree less than k to obtain the core of a complex network. The simplicity and effectiveness of this approach has led to a variety of applications in many scientific fields, including bioinformatics, neurosciences, computer sciences, economics, and network sciences. However, the analytical theory of the k-core pruning process is still lacking. Here we find that in every pruning step of any given network, the Non-Backtracking Expansion Branch (NBEB) is directly related to the remaining k-core. Using this NBEB method, we obtain the analytical results of the k-core pruning process and its detailed critical behaviour.
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Key words
Complex system,Complex network,Node ranking,k-core,Phase transition
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