Formula omitted]-sequences and 2-step coreness in graphs

Abstract

An H-sequence of a vertex is defined by iteratively applying H-index to neighbors of the vertex in a graph. It is still not known whether changing the initial values affects the convergence of H-sequences. Our purpose is to investigate the properties of H-sequences initialized with arbitrary positive integers. This paper presents the necessary and sufficient conditions for the convergence of H-sequences. Theoretical results reveal the differences between divergent H-sequences of infinite graphs and finite graphs. Divergent H-sequences of infinite graphs are either periodic or non-periodic, whereas divergent H-sequences of finite graphs must be periodic with a period of 2.Based on H-sequences, we define 2-step coreness on the second-order neighbors of a vertex. A new centrality is proposed by combining classical coreness and 2-step coreness. The new centrality captures a wider range of information in a network. Experimental results show that the proposed centrality makes significant improvements over centralities such as betweenness, H-index and coreness.