Spectral partitioning for node criticality

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract-Finding critical nodes in a network is a significant task, highly relevant to network vulnerability and security. We consider the node criticality problem as an algebraic connectivity minimization problem where the objective is to choose nodes which minimize the algebraic connectivity of the resulting network. Previous suboptimal solutions of the problem suffer from the computational complexity associated with the implementation of a maximization consensus algorithm. In this work, we use spectral partitioning concepts introduced by Fiedler, to propose a new suboptimal solution which significantly reduces the implementation complexity. Our approach, combined with recently proposed distributed Fiedler vector calculation algorithms enable each node to decide by itself whether it is a critical node. If a single node is required then the maximization algorithm is applied on a restricted set of nodes within the network. We derive a lower bound for the achievable algebraic connectivity when nodes are removed from the network and we show through simulations that our approach leads to algebraic connectivity values close to this lower bound. Similar behaviour is exhibited by other approaches at the expense, however, of a higher implementation complexity. Permanent repository link

Optimization based spectral partitioning for node criticality assessment

“…Among the nodes which lie in the sign cut-set how do we choose the one which is the most critical? In our recent work in [37] we have chosen the node which maximizes the sum of squared…”

“…The criticality of a fixed number of nodes is assessed by evaluating the degradation in performance achieved when these nodes are removed from the network. We conduct a comparative study to investigate the performance of the proposed metric against other approaches that exist in literature such as the betweenness centrality [20], the closeness centrality, the degree centrality [16], the exhaustive search approach, the Hybrid Interactive Linear Programming Rounding (HILPR) metric proposed in [13], the Controllability of complex networks (Cont) approach in [18], the suboptimal solution of Eq (6) which we refer to as the Sum Squared Difference approach (SSD) [28] [29], the suboptimal solution of Eq (7) which we refer to as the Normalized Sum Squared Difference approach (NSSD) [30][31] and our previously proposed approach which we refer to as Spectral Partitioning for Node Criticality approach (SPNC) [37]. Our simulation results indicate that the suboptimal solutions are not conservative and that the proposed criticality metric chooses the most critical nodes in the network as it achieves the greatest degradation in performance when these nodes are removed.…”

“…We conduct the simulation experiments on the Ns-3 Simulator [53] and evaluate the network performance using network centric performance criteria such as the total network throughput, the average per packet delay, the average per packet jitter and the total number of packets dropped. In all the simulations we compare the performance of the proposed metric against metrics such as, betweenness centrality, closeness centrality, degree centrality, Hybrid Interactive Linear Programming Rounding (HILPR), the Controllability of complex networks (Cont),the Sum Squared Difference (SSD) approach, the Normalized Sum Squared Difference (NSSD) approach and the previously proposed Spectral Partitioning for Node Criticality (SPNC) approach [37].…”

“…As pointed out above, the proposed change of sign method can lead to multiple nodes being detected as critical and so, when a single node is required, a metric must be utilized to decide on the most critical node among the ones which lie on the boundary of the Fiedler clusters. In our recent work in [37], we have adopted the metric in [30] [31], however, in this work we consider an alternative metric which takes into account the users of the underlying network and their source destination paths. The algebraic connectivity depends only on the topology of the underlying network and the criticality metric must thus be complemented to account for the intuitive notion that the users of the network must also be taken into consideration when assessing the criticality of a node.…”

Node Criticality Assessment in a Blockchain Network

“…The proposed approach deems a node as critical if it lies in a cutset and experiences the highest traffic flow. A cutset is defined as a set of nodes, that observe a change in sign for the Fiedler vector among their neighbours [2]. The proposed approach is evaluated for change in blockchain size and packet drop ratios and it is observed that the proposed approach outperforms existing approaches by showing a greater reduction in blockchain size and a larger packet drop rate upon removal of the most critical nodes from the network.…”