Efficiently identifying critical nodes in large complex networks

Abstract

The critical node detection problem (CNDP) aims to fragment a graph G = (V, E) by removing a set of vertices R with cardinality |R| ≤ k, such that the residual graph has minimum pairwise connectivity for user-defined value k. Existing optimization algorithms are incapable of finding a good set R in graphs with many thousands or millions of vertices due to the associated computational cost. Hence, there exists a need for a time-and space-efficient approach for evaluating the impact of removing any v ∈ V in the context of the CNDP. In this paper, we propose an algorithm based on a modified depth-first search that requires O(k(|V| + |E|)) time complexity. We employ the method within in a greedy algorithm for quickly identifying R. Our experimental results consider small-(≤ 250 nodes) and medium-sized (≤ 25, 000 nodes) networks, where it is possible to compare to known optimal solutions or results obtained by other heuristics. Additionally, we show results using six real-world networks. The proposed algorithm can be easily extended to vertex-and edge-weighted variants of the CNDP.

PFCA: An influence‐based parallel fuzzy clustering algorithm for large complex networks

“…The connections among various entities of big data collectively form complex networks. A complex network is a graph that has significant topological features, which are common in real‐life networks of various domains such as biological networks (Mason & Verwoerd, ), social networks (Boccaletti, Latora, Moreno, Chavez, & Hwang, ; Ventresca & Aleman, ; L. Wang & Hopcroft, ), and collaboration networks (Long, Cunningham, Carswell, & Braithwaite, ).…”

Computing Critical Nodes in Directed Graphs

“…We refer to this heuristic also as MCN since there is no risk of confusion. In addition to that, we considered the following three heuristics which were among the top performers in the experiments on undirected graphs by Ventresca and Aleman [25]: Maximum degree (MAX-DEG). This heuristic repeatedly removes a vertex of maximum degree.…”

“…In the special case of k = 1, we wish to locate a vertex x ∈ V such that f (G \ x) is minimum. We refer to such a vertex x as the most critical node of G. This problem was previously considered in the literature, but only for undirected graphs (see, e.g., [3,25]). In particular, Ventresca and Aleman [25] presented a linear-time algorithm for the k = 1 case in undirected graphs.…”

“…We refer to such a vertex x as the most critical node of G. This problem was previously considered in the literature, but only for undirected graphs (see, e.g., [3,25]). In particular, Ventresca and Aleman [25] presented a linear-time algorithm for the k = 1 case in undirected graphs. Their algorithm exploits the relation between depth-first search (dfs) and articulation points and biconnected components of an undirected graph G [22].…”

“…Problems of this type have received a lot of attention recently: for example, one may wish to identify nodes that represent highly influential individuals in a social network [17], or locations in a network that are useful in order to inhibit diffusion of contagions [4,19], or to assess network vulnerabilities [21]. Motivated by the recent study of Ventresca and Aleman [25], we consider the problem of detecting a set S of critical nodes such that G \ S has minimum pairwise strong connectivity. This problem is NP-hard [3,11], and thus we are interested in practical heuristics.…”