The Impact of Edge Deletions on the Number of Errors in Networks

Abstract

Abstract. In this paper, we deal with an error model in distributed networks. For a target t, every node is assumed to give an advice, ie.to point to a neighbour that take closer to the destination. Any node giving a bad advice is called a liar . Starting from a situation without any liar, we study the impact of topology changes on the number of liars. More precisely, we establish a relationship between the number of liars and the number of distance changes after one edge deletion. Whenever deleted edges are chosen uniformly at random, for any graph with n nodes, m edges and diameter D, we prove that the expected number of liars and distance changes is O( 2 Dn m ) in the resulting graph. The result is tight for = 1. For some specific topologies, we give more precise bounds.

Stepping Back from the Trees to See the Forest: Network Approaches to Valuing Intelligence

“…There has been a number of works exploring this question. 95,96,97,98 The end results are that for most traditional centrality metrics, networks are largely resilient to minimal node deletion. Of course we would like to explore this effect in other networks with additional metrics.…”

“…They then gained a confidence interval around some centrality scores to measure robustness of the scores 85. Glacet et al used deletion of edges to measure the effect of topology on the number of liars one might expect to encounter in a network of advice givers on directions 86. These deletion techniques tend to be focused on the purposes of the graph or testing the resiliency of different measures.…”