How Members of Covert Networks Conceal the Identities of Their Leaders

Centrality measures are the most commonly advocated social network analysis tools for identifying leaders of covert organizations. While the literature has predominantly focused on studying the effectiveness of existing centrality measures or developing new ones, we study the problem from the opposite perspective, by focusing on how a group of leaders can avoid being identified by centrality measures as key members of a covert network. More specifically, we analyze the problem of choosing a set of edges to be added to a network to decrease the leaders’ ranking according to three fundamental centrality measures, namely, degree, closeness, and betweenness. We prove that this problem is NP-complete for each measure. Moreover, we study how the leaders can construct a network from scratch, designed specifically to keep them hidden from centrality measures. We identify a network structure that not only guarantees to hide the leaders to a certain extent but also allows them to spread their influence across the network.

Enemies in the Shadows: On the Origins and Survival of Clandestine Clients

States often use covert operations to undermine their adversaries. This strategy involves, among other methods, intelligence organizations directing and supporting the operations of covert networks residing within the target state. This was a common occurrence during the Cold War, but covert clients also operate in modern conflicts in Syria, Ukraine, and elsewhere. This paper introduces and defines covert clients as a distinct and novel concept. We then use original data on more than 250 clandestine networks within the French Resistance to investigate the determinants of covert client success and failure. We find that clients founded by foreign operatives inserted into the target state fail at significantly higher rates than those that establish themselves organically within the target state, although this effect diminishes among stronger groups. We corroborate these findings with a case study of the Prosper network to demonstrate how clandestine group origins influence their local knowledge, incentives, and security practices. This study uses original data to provide novel insights into clandestine group survival by linking survival to group origins. In demonstrating the potential utility of focusing on the conduct of covert operations, we also contribute to a rapidly growing international relations literature on how states project power through covert action.

Optimal Surveillance of Covert Networks by Minimizing Inverse Geodesic Length

The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices. In network analysis, IGL of a network is often used to assess and evaluate how well heuristics perform in strengthening or weakening a network. We consider the edge-deletion problem MINIGLED. Formally, given a graph G, a budget k, and a target inverse geodesic length T, the question is whether there exists a subset of edges X with |X| ≤ ck, such that the inverse geodesic length of G − X is at most T.In this paper, we design algorithms and study the complexity of MINIGL-ED. We show that it is NP-complete and cannot be solved in subexponential time even when restricted to bipartite or split graphs assuming the Exponential Time Hypothesis. In terms of parameterized complexity, we consider the problem with respect to various parameters. We show that MINIGL-ED is fixed-parameter tractable for parameter T and vertex cover by modeling the problem as an integer quadratic program. We also provide FPT algorithms parameterized by twin cover and neighborhood diversity combined with the deletion budget k. On the negative side we show that MINIGL-ED is W[1]-hard for parameter tree-width.

Attachment Centrality for Weighted Graphs

Measuring how central nodes are in terms of connecting a network has recently received increasing attention in the literature. While a few dedicated centrality measures have been proposed, Skibski et al. [2016] showed that the Attachment Centrality is the only one that satisfies certain natural axioms desirable for connectivity. Unfortunately, the Attachment Centrality is defined only for unweighted graphs which makes this measure ill-fitted for various applications. For instance, covert networks are typically weighted, where the weights carry additional intelligence available about criminals or terrorists and the links between them. To analyse such settings, in this paper we extend the Attachment Centrality to node-weighted and edge-weighted graphs. By an axiomatic analysis, we show that the Attachment Centrality is closely related to the Degree Centrality in weighted graphs.

Weakening Covert Networks by Minimizing Inverse Geodesic Length

We consider the problem of deleting nodes in a covert network to minimize its performance. The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices. In the MinIGL problem the input is a graph $G$, a budget $k$, and a target IGL $T$, and the question is whether there exists a subset of vertices $X$ with $|X|=k$, such that the IGL of $G-X$ is at most $T$. In network analysis, the IGL is often used to evaluate how well heuristics perform in strengthening or weakening a network. In this paper, we undertake a study of the classical and parameterized complexity of the MinIGL problem. The problem is NP-complete even if $T=0$ and remains both NP-complete and $W[1]$-hard for parameter $k$ on bipartite and on split graphs. On the positive side, we design several multivariate algorithms for the problem. Our main result is an algorithm for MinIGL parameterized by the twin cover number.