Abstract
Identifying vital nodes in complex networks is a critical problem in the field of network theory. To this end, the Collective Influence (CI) algorithm has been introduced and shows high efficiency and scalability in searching for the influential nodes in the optimal percolation model. However, the crucial part of the CI algorithm, reinsertion, has not been significantly investigated or improved upon. In this paper, the author improves the CI algorithm and proposes a new algorithm called Collective-Influence-Disjoint-Set-Reinsertion (CIDR) based on disjoint-set reinsertion. Experimental results on 8 datasets with scales of a million nodes and 4 random graph networks demonstrate that the proposed CIDR algorithm outperforms other algorithms, including Betweenness centrality, Closeness centrality, PageRank centrality, Degree centrality (HDA), Eigenvector centrality, Nonbacktracking centrality and Collective Influence with original reinsertion, in terms of the Robustness metric. Moreover, CIDR is applied to an international competition on optimal percolation and ultimately ranks in 7th place.
Highlights
Identifying vital nodes in complex networks is a critical problem in the field of network theory
A scalable theoretical framework called the Collective Influence (CI) algorithm, which attempts to find the minimal fraction of nodes that can fragment the network in optimal percolation, was recently proposed[4]
After the newly proposed algorithm CIDR is applied, even CIDR employing a radius of 0 is capable of achieving a better result. This indicator shows that the proposed disjoint-set reinsertion in CIDR is able to achieve better Robustness compared to Original Reinsertion
Summary
Identifying vital nodes in complex networks is a critical problem in the field of network theory To this end, the Collective Influence (CI) algorithm has been introduced and shows high efficiency and scalability in searching for the influential nodes in the optimal percolation model. Experimental results on 8 datasets with scales of a million nodes and 4 random graph networks demonstrate that the proposed CIDR algorithm outperforms other algorithms, including Betweenness centrality, Closeness centrality, PageRank centrality, Degree centrality (HDA), Eigenvector centrality, Nonbacktracking centrality and Collective Influence with original reinsertion, in terms of the Robustness metric. Nonbacktracking centrality[24] modified the standard Eigenvector centrality based on the Nonbacktracking matrix to ignore the reflection mechanism on hubs, therein being asymptotically equivalent to Eigenvector centrality for dense networks and avoiding hub localization on sparse networks For these methods, the node importance is evaluated by regarding a node as an isolated agent in a non-interacting setting. For networks with millions of nodes, such as massive social media and social networks[22], CI performs well in processing centrality efficiently
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