Analyzing R-Robustness of Random K-Out Graphs for the Design of Robust Networks

Eray Can Elumar, Osman Yagan

Abstract: We consider a graph property known as $r$-robustness, a robustness metric that plays a key role in analyzing consensus dynamics. It was previously shown that in the presence of adversarial nodes, consensus can be reached in an $r$-robust network for sufficiently large $r$. Further, $r$-robustness is a stronger property than $r$-connectivity, hence it is also useful in many applications where robustness of networks to disruptions such as adversarial attacks or node failures is of practical interest. In this paper, we study $r$-robustness of random K-out graphs, which have been used in many applications including random (pairwise) key predistribution in wireless sensor networks, anonymous message routing in crypto-currency networks, and differentially-private federated averaging. Significantly improving an earlier result, we provide a set of conditions for $K$ and $n$ that ensure, with high probability (whp), the $r$-robustness of the random K-out graph. Simulation results are used to verify the results. To demonstrate the viability of our results in practical applications, we compare our results with the results from Erdös-Rényi and the Barabási-Albert random graph models.

External IDs:dblp:conf/icc/ElumarY23