Node diversification in complex networks by decentralized colouring

Abstract

We develop a decentralized coloring approach to diversify the nodes in a complex network. The key is the introduction of a local conflict index that measures the color conflicts arising at each node which can be efficiently computed using only local information. We demonstrate via both synthetic and realworld networks that the proposed approach significantly outperforms random coloring as measured by the size of the largest color-induced connected component. Interestingly, for scale-free networks further improvement of diversity can be achieved by tuning a degree-biasing weighting parameter in the local conflict index.

Quantifying Cybersecurity Effectiveness of Dynamic Network Diversity

“…Prior studies in network diversity. Network diversity has been investigated in some contexts [1], [2], [3], [32], [33]. There are proposals on measuring static network diversity via (i) the entropy of the distribution of software vulnerability in a network [38] and (ii) the diversity index of the shared vulnerabilities between different software implementations in a network [41].…”

“…There are proposals on measuring static network diversity via (i) the entropy of the distribution of software vulnerability in a network [38] and (ii) the diversity index of the shared vulnerabilities between different software implementations in a network [41]. There are attempts at optimizing static diversity by using some flavor of graph coloring algorithm (i.e., treating a diversified implementation as a color and a network as a graph) and minimizing defective edges (i.e., adjacent nodes have the same color or run the same software implementation) [32], [33], [34], [35], [36], [37].…”

“…The preceding question leads to the notion of network diversity, which deals with the employment of diversified program implementations in network-wide software stacks [1], [2], [3], [32], [33]. A simpler version of the notion may be called static diversity, where diversified implementations are employed once and for all (i.e., unchanged after initial employment).…”

“…A simpler version of the notion may be called static diversity, where diversified implementations are employed once and for all (i.e., unchanged after initial employment). There are studies on optimizing static diversity via some flavor of graph coloring algorithm; by treating colors as diversified implementations, the research problem is to minimize defective edges (i.e., adjacent nodes have the same color or run the same implementation) [32], [33], [34], [35], [36], [37]. There are also studies on quantifying the effectiveness of static diversity [37], [38], [39], [40], [41].…”

The resistance perturbation distance: A metric for the analysis of dynamic networks

“…The algorithm for the fast computation of the d rp 2 distance is described in Algorithm 2. A MATLAB implementation of Spielman and Srivastava's algorithm written by Richard Garcia-Lebron was used [21] to compute Algorithm 1. The code utilizes an implementation of the combinatorial multigrid solver [28] written by Ioannis Koutis, and Gary Miller.…”