Detecting Core-Periphery Structures by Surprise

Detecting the presence of mesoscale structures in complex networks is of primary importance. This is especially true for financial networks, whose structural organization deeply affects their resilience to events like default cascades, shocks propagation, etc. Several methods have been proposed, so far, to detect communities, i.e. groups of nodes whose connectivity is significantly large. Communities, however do not represent the only kind of mesoscale structures characterizing real-world networks: other examples are provided by bow-tie structures, core-periphery structures and bipartite structures. Here we propose a novel method to detect statistically-signifcant bimodular structures, i.e. either bipartite or core-periphery ones. It is based on a modification of the surprise, recently proposed for detecting communities. Our variant allows for bimodular nodes partitions to be revealed, by letting links to be placed either 1) within the core part and between the core and the periphery parts or 2) just between the (empty) layers of a bipartite network. From a technical point of view, this is achieved by employing a multinomial hypergeometric distribution instead of the traditional (binomial) hypergeometric one; as in the latter case, this allows a p-value to be assigned to any given (bi)partition of the nodes. To illustrate the performance of our method, we report the results of its application to several real-world networks, including social, economic and financial ones.Comment: 11 pages, 10 figures. Python code freely available at https://github.com/jeroenvldj/bimodular_surpris

Resilience or robustness : identifying topological vulnerabilities in rail networks

Many critical infrastructure systems have network structure and are under stress. Despite their national importance, the complexity of large-scale transport networks means we do not fully understand their vulnerabilities to cascade failures. The research in this paper examines the interdependent rail networks in Greater London and surrounding commuter area. We focus on the morning commuter hours, where the system is under the most demand stress. There is increasing evidence that the topological shape of the network plays an important role in dynamic cascades. Here, we examine whether the different topological measures of resilience (stability) or robustness (failure) are more appropriate for understanding poor railway performance. The results show that resilience and not robustness has a strong correlation to the consumer experience statistics. Our results are a way of describing the complexity of cascade dynamics on networks without the involvement of detailed agent-based-models, showing that cascade effects are more responsible for poor performance than failures. The network science analysis hints at pathways towards making the network structure more resilient by reducing feedback loops

Post-Mortem Examination of the International Financial Network

As the recent crisis has forcefully suggested, understanding financial-market interconnectedness is of a paramount importance to explain systemic risk, stability and economic dynamics. In this paper, we address these issues along two related perspectives. First, we explore the statistical properties of the International Financial Network (IFN), defined as the weighted-directed multigraph where nodes are world countries and links represent debtor-creditor relationships in equities and short/long-run debt. We investigate whether the 2008 financial crisis has resulted in a significant change in the topological properties of the IFN. Our findings suggest that the crisis caused not only a reduction in the amount of securities traded, but also induced changes in the topology of the network and in the time evolution of its statistical properties. This has happened, however, without changing the disassortative, core-periphery structure of the IFN architecture. Second, we perform an econometric study to examine the ability of network-based measures to explain cross-country differences in crisis intensity. We investigate whether the conclusion of previous studies showing that international connectedness is not a relevant predictor of crisis intensity may be reversed, once one explicitly accounts for the position of each country within the IFN. We show that higher interconnectedness reduces the severity of the crisis, as it allows adverse shocks to dissipate quicker. However, the systemic risk hypothesis cannot be completely dismissed and being central in the network, if the node is not a member of a rich club, puts the country in an adverse and risky position in times of crises. Finally, we find strong evidence of nonlinear effects, once the high degree of heterogeneity that characterizes the IFN is taken into account.financial networks, crisis, early warning systems

Advances on the Resilience of Complex Networks

n/