Fundamental difference between superblockers and superspreaders in networks

TL;DR

This paper investigates the difference between superblockers and superspreaders in networks, demonstrating through extensive analysis that the two roles are not interchangeable and serve different functions in network dynamics.

Contribution

The study provides the first empirical validation that superblockers and superspreaders are distinct, challenging the conjecture of their equivalence in network optimization.

Findings

Superblockers do not act as optimal spreaders.

The two problems are fundamentally different in real-world networks.

Empirical evidence refutes the conjecture of their equivalence.

Abstract

Two very important problems regarding spreading phenomena in complex topologies are the optimal selection of node sets either to minimize or maximize the extent of outbreaks. Both problems are nontrivial when a small fraction of the nodes in the network can be used to achieve the desired goal. The minimization problem is equivalent to a structural optimization. The "superblockers", i.e., the nodes that should be removed from the network to minimize the size of outbreaks, are those nodes that make connected components as small as possible. "Superspreaders" are instead the nodes such that, if chosen as initiators, they maximize the average size of outbreaks. The identity of superspreaders is expected to depend not just on the topology, but also on the specific dynamics considered. Recently, it has been conjectured that the two optimization problems might be equivalent, in the sense that superblockers act also as superspreaders. In spite of its potential groundbreaking importance, no empirical study has been performed to validate this conjecture. In this paper, we perform an extensive analysis over a large set of real-world networks to test the similarity between sets of superblockers and of superspreaders. We show that the two optimization problems are not equivalent: superblockers do not act as optimal spreaders.