Node importance measurement based on neighborhood similarity in complex network

Abstract

Ranking node importance is of great significance for studying the robustness and vulnerability of complex network. Over the recent years, various centrality indices such as degree, semilocal, K-shell, betweenness and closeness centrality have been employed to measure node importance in the network. Among them, some well-known global measures such as betweenness centrality and closeness centrality can achieve generally higher accuracy in ranking nodes, while their computation complexity is relatively high, and also the global information is not readily available in a large-scaled network. In this paper, we propose a new local metric which only needs to obtain the neighborhood information within two hops of the node to rank node importance. Firstly, we calculate the similarity of node neighbors by quantifying the overlap of their topological structures with Jaccard index; secondly, the similarity between pairs of neighbor nodes is calculated synthetically, and the redundancy of the local link of nodes is obtained. Finally, by reducing the influence of densely local links on ranking node importance, a new local index named LLS that considers both neighborhood similarity and node degree is proposed. To check the effectiveness of the proposed method of ranking node importance, we carry out it on six real world networks and one artificial small-world network by static attacks and dynamic attacks. In the static attack mode, the ranking value of each node is the same as that in the original network. In the dynamic attack mode, once the nodes are removed, the centrality of each node needs recalculating. The relative size of the giant component and the network efficiency are used for network connectivity assessment during the attack. A faster decrease in the size of the giant component and a faster decay of network efficiency indicate a more effective attack strategy. By comparing the decline rates of these two indices to evaluate the connectedness of all networks, we find that the proposed method is more efficient than traditional local metrics such as degree centrality, semilocal centrality, K-shell decomposition method, no matter whether it is in the static or dynamic manner. And for a certain ranking method, the results of the dynamic attack are always better than those of the static attack. This work can shed some light on how the local densely connections affect the node centrality in maintaining network robustness.

Structural Robustness of Complex Networks: A Survey of A Posteriori Measures

“…2) Topology-based Attack Strategies: Beside degree and betweenness, commonly-used measures of importance include closeness [99], Katz centrality [100], neighborhood similarity [101], branch weighting [102], structural holes [103], and so on. However, ranking the importance of nodes or edges is practically intractable for large-scale networks, since most measures cannot guarantee that removing the targeted object will globally and consistently cause the greatest damage to the network.…”

Edge-weights-based method to identify influential spreaders in complex networks

“…The identification of influential spreaders in complex networks is of great significance in both theory and application in such domains as social network analysis (Purevsuren and Cui, 2019; Yang et al, 2018), efficient dissemination of information (Lü et al, 2011; Medo et al, 2009), containment of disease spread (Wang et al, 2015b; Wei et al, 2022), control of rumors (Gu and Xia, 2012) and virus spread (Morone et al, 2016; Pinheiro et al, 2021; Wang et al, 2015a), and so on. At present, many influential spreaders identification methods have been proposed (Bonacich, 1972; Freeman, 1977, 1978; Kitsak et al, 2010; Li et al, 2019, 2020; Lü et al, 2016; Ren et al, 2023; Ruan et al, 2017).…”

Influence of Removing Leaf Node Neighbors on Network Controllability

“…For example, the node with the highest degree is attacked firstly or the edge with the highest betweenness is preferentially removed. Besides degree and betweenness, commonly used measures of node importance include closeness [ 9 ], Katz centrality [ 10 ], neighborhood similarity [ 11 ], branch weighting [ 12 ], structural holes [ 13 ], and so on. Many malicious attack models have been proposed; the hierarchical structure of a directed network enables a random upstream (or downstream) attack on the network controllability, which results in a more destructive attack strategy than random attacks [ 14 ].…”