Where Graph Topology Matters: The Robust Subgraph Problem

Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall vulnerability to external attacks or random failures. In this paper, we turn attention to local robustness and pose a novel problem in the lines of subgraph mining: given a large graph, how can we find its most robust local subgraph (RLS)? We define a robust subgraph as a subset of nodes with high communicability among them, and formulate the RLS-PROBLEM of finding a subgraph of given size with maximum robustness in the host graph. Our formulation is related to the recently proposed general framework for the densest subgraph problem, however differs from it substantially in that besides the number of edges in the subgraph, robustness also concerns with the placement of edges, i.e., the subgraph topology. We show that the RLS-PROBLEM is NP-hard and propose two heuristic algorithms based on top-down and bottom-up search strategies. Further, we present modifications of our algorithms to handle three practical variants of the RLS-PROBLEM. Experiments on synthetic and real-world graphs demonstrate that we find subgraphs with larger robustness than the densest subgraphs even at lower densities, suggesting that the existing approaches are not suitable for the new problem setting.Comment: 13 pages, 10 Figures, 3 Tables, to appear at SDM 2015 (9 pages only

Systemic trade-risk of critical resources

In the wake of the 2008 financial crisis the role of strongly interconnected markets in fostering systemic instability has been increasingly acknowledged. Trade networks of commodities are susceptible to deleterious cascades of supply shocks that increase systemic trade-risks and pose a threat to geopolitical stability. On a global and a regional level we show that supply risk, scarcity, and price volatility of non-fuel mineral resources are intricately connected with the structure of the world-trade network of or spanned by these resources. On the global level we demonstrate that the scarcity of a resource, as measured by its trade volume compared to extractable reserves, is closely related to the susceptibility of the trade network with respect to cascading shocks. On the regional level we find that to some extent the region-specific price volatility and supply risk can be understood by centrality measures that capture systemic trade-risk. The resources associated with the highest systemic trade-risk indicators are often those that are produced as byproducts of major metals. We identify significant shortcomings in the management of systemic trade-risk, in particular in the EU

Mathematics and the Internet: A Source of Enormous Confusion and Great Potential

Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type

Architecture-based Qualitative Risk Analysis for Availability of IT Infrastructures

An IT risk assessment must deliver the best possible quality of results in a time-effective way. Organisations are used to customise the general-purpose standard risk assessment methods in a way that can satisfy their requirements. In this paper we present the QualTD Model and method, which is meant to be employed together with standard risk assessment methods for the qualitative assessment of availability risks of IT architectures, or parts of them. The QualTD Model is based on our previous quantitative model, but geared to industrial practice since it does not require quantitative data which is often too costly to acquire. We validate the model and method in a real-world case by performing a risk assessment on the authentication and authorisation system of a large multinational company and by evaluating the results w.r.t. the goals of the stakeholders of the system. We also perform a review of the most popular standard risk assessment methods and an analysis of which one can be actually integrated with our QualTD Model

CBDI: Combined Banzhaf & Diversity Index for Finding Critical Nodes

Critical node discovery plays a vital role in assessing the vulnerability of a network to an abrupt change, such as an adversarial attack or human intervention. In this paper, we propose a new metric to characterize the criticality of a node in an arbitrary network which we refer to as the Combined Banzhaf & Diversity Index (CBDI). The metric utilizes a diversity index which is based on the variability of a node’s attributes relative to its neighbors and the Banzhaf Power Index which characterizes the degree of participation of a node in forming shortest paths. The Banzhaf power index is inspired from the theory of voting games in game theory. We evaluate the performance of the new metric using simulations. Our results indicate that in a number of network topologies, the proposed metric outperforms other proposals which have appeared in the literature. The proposed CBDI index chooses more critical nodes which, when removed, degrade network performance to a greater extent than if critical nodes based on other criticality metrics were removed

Critical Node Identifcation for accessing network vulnerability, a necessary consideration

Timely identification of critical nodes is crucial for assessing network vulnerability and survivability. This thesis presents two new approaches for the identification of critical nodes in a network with the first being an intuition based approach and the second being build on a mathematical framework. The first approach which is referred to as the Combined Banzhaf & Diversity Index (CBDI) uses a newly devised diversity metric, that uses the variability of a node’s attributes relative to its neighbours and the Banzhaf power index which characterizes the degree of participation of a node in forming the shortest path route. The Banzhaf power index is inspired from the theory of voting games in game theory whereas, the diversity index is inspired from the analysis and understanding of the influence of the average path length of a network on its performance. This thesis also presents a new approach for evaluating this average path length metric of a network with reduced computational complexity and proposes a new mechanism for reducing the average path length of a network for relatively larger network structures. The proposed average path length reduction mechanism is tested for a wireless sensor network and the results compared for multiple existing approaches. It has been observed using simulations that, the proposed average path length reduction mechanism outperforms existing approaches by reducing the average path length to a greater extent and with a simpler hardware requirement. The second approach proposed in this thesis for the identification of critical nodes is build on a mathematical framework and it is based on suboptimal solutions of two optimization problems, namely the algebraic connectivity minimization problem and a min-max network utility problem. The former attempts to address the topological as- pect of node criticality whereas, the latter attempts to address its connection-oriented nature. The suboptimal solution of the algebraic connectivity minimization problem is obtained through spectral partitioning considerations. This approach leads to a distributed solution which is computationally less expensive than other approaches that exist in the literature and is near optimal, in the sense that it is shown through simulations to approximate a lower bound which is obtained analytically. Despite the generality of the proposed approaches, this thesis evaluates their performance on a wireless ad hoc network and demonstrates through extensive simulations that the proposed solutions are able to choose more critical nodes relative to other approaches, as it is observed that when these nodes are removed they lead to the highest degrada- tion in network performance in terms of the achieved network throughput, the average network delay, the average network jitter and the number of dropped packets

Combined Banzhaf & Diversity Index (CBDI) for critical node detection

Critical node discovery plays a vital role in assessing the vulnerability of a computer network to malicious attacks and failures and provides a useful tool with which one can greatly improve network security and reliability. In this paper, we propose a new metric to characterize the criticality of a node in an arbitrary computer network which we refer to as the Combined Banzhaf & Diversity Index (CBDI). The metric utilizes a diversity index which is based on the variability of a node׳s attributes relative to its neighbours and the Banzhaf power index which characterizes the degree of participation of a node in forming shortest paths. The Banzhaf power index is inspired from the theory of voting games in game theory. The proposed metric is evaluated using analysis and simulations. The criticality of nodes in a network is assessed based on the degradation in network performance achieved when these nodes are removed. We use several performance metrics to evaluate network performance including the algebraic connectivity which is a spectral metric characterizing the connectivity robustness of the network. Extensive simulations in a number of network topologies indicate that the proposed CBDI index chooses more critical nodes which, when removed, degrade network performance to a greater extent than if critical nodes based on other criticality metrics were removed