Whether as telecommunications or power systems, networks are very important in everyday life. Maintaining these networks properly functional and connected, even under attacks or failures, is of special concern. This topic has been previously studied with a whole network robustness perspective,modeling networks as undirected graphs (such as roads or simply cables). This perspective measures the average behavior of the network after its last node has failed. In this article we propose two alternatives to well-known studies about the robustness of the backbone Internet: to use a supply network model and metrics for its representation (we called it the Go-Index), and to use robustness metrics that can be calculated while disconnections appear. Our research question is: if a smart adversary has a limited number of strikes to attack the Internet, how much will the damage be after each one in terms of network disconnection? Our findings suggest that in order to design robust networks it might be better to have a complete view of the robustness evolution of the network, from both the infrastructure and the users perspective.
On @cite_4 was found that targeted attack can be more effective when they are directed to bottlenecks rather than hubs. On @cite_18 authors present partial values of @math -index while nodes are disconnected, showing the importance of a well chosen robustness metric for performing the attacks.
@cite_18 @cite_4
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In this article we present Miuz, a robustness index for complex networks. Miuz measures the impact of disconnecting a node from the network while comparing the sizes of the remaining connected components. Strictly speaking, Miuz for a node is defined as the inverse of the size of the largest connected component divided by the sum of the sizes of the remaining ones. We tested our index in attack strategies where the nodes are disconnected in decreasing order of a specified metric. We considered Miuz and other well-known centrality measures such as betweenness, degree, and harmonic centrality. All of these metrics were compared regarding the behavior of the robustness (R- index) during the attacks. In an attempt to simulate the internet backbone, the attacks were performed in complex networks with power-law degree distributions (scale-free networks). Preliminary results show that attacks based on disconnecting a few number of nodes Miuz are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that Miuz, as well as other measures based on the size of the largest connected component, provides a good addition to other robustness metrics for complex networks. We study the property of certain complex networks of being both sparse and highly connected, which is known as “good expansion” (GE). A network has GE properties if every subset S of nodes (up to 50 of the nodes) has a neighborhood that is larger than some “expansion factor” φ multiplied by the number of nodes in S. Using a graph spectral method we introduce here a new parameter measuring the good expansion character of a network. By means of this parameter we are able to classify 51 real-world complex networks — technological, biological, informational, biological and social — as GENs or non-GENs. Combining GE properties and node degree distribution (DD) we classify these complex networks in four different groups, which have different resilience to intentional attacks against their nodes. The simultaneous existence of GE properties and uniform degree distribution contribute significantly to the robustness in complex networks. These features appear solely in 14 of the 51 real-world networks studied here. At the other extreme we find that ∼40 of all networks are very vulnerable to targeted attacks. They lack GE properties, display skewed DD — exponential or power-law — and their topologies are changed more dramatically by targeted attacks directed at bottlenecks than by the removal of network hubs.