How Damage Diversification Can Reduce Systemic Risk

We consider the problem of risk diversification in complex networks. Nodes represent e.g. financial actors, whereas weighted links represent e.g. financial obligations (credits/debts). Each node has a risk to fail because of losses resulting from defaulting neighbors, which may lead to large failure cascades. Classical risk diversification strategies usually neglect network effects and therefore suggest that risk can be reduced if possible losses (i.e., exposures) are split among many neighbors (exposure diversification, ED). But from a complex networks perspective diversification implies higher connectivity of the system as a whole which can also lead to increasing failure risk of a node. To cope with this, we propose a different strategy (damage diversification, DD), i.e. the diversification of losses that are imposed on neighboring nodes as opposed to losses incurred by the node itself. Here, we quantify the potential of DD to reduce systemic risk in comparison to ED. For this, we develop a branching process approximation that we generalize to weighted networks with (almost) arbitrary degree and weight distributions. This allows us to identify systemically relevant nodes in a network even if their directed weights differ strongly. On the macro level, we provide an analytical expression for the average cascade size, to quantify systemic risk. Furthermore, on the meso level we calculate failure probabilities of nodes conditional on their system relevance

Oscillations of complex networks

A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how such a network responds to sudden changes caused by attacks or disturbances. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to \emph{oscillate} persistently in the sense that the characterizing quantities vary periodically or randomly with time. We provide a theoretical estimate of the critical capacity-parameter value for the onset of the network oscillation. The finding is expected to have broad implications as it suggests that complex networks may be structurally highly dynamic.Comment: 4 pages, 4 figures. submitte

On the Convexity of Latent Social Network Inference

In many real-world scenarios, it is nearly impossible to collect explicit social network data. In such cases, whole networks must be inferred from underlying observations. Here, we formulate the problem of inferring latent social networks based on network diffusion or disease propagation data. We consider contagions propagating over the edges of an unobserved social network, where we only observe the times when nodes became infected, but not who infected them. Given such node infection times, we then identify the optimal network that best explains the observed data. We present a maximum likelihood approach based on convex programming with a l1-like penalty term that encourages sparsity. Experiments on real and synthetic data reveal that our method near-perfectly recovers the underlying network structure as well as the parameters of the contagion propagation model. Moreover, our approach scales well as it can infer optimal networks of thousands of nodes in a matter of minutes.Comment: NIPS, 201

Contextual Centrality: Going Beyond Network Structures

Centrality is a fundamental network property which ranks nodes by their structural importance. However, structural importance may not suffice to predict successful diffusions in a wide range of applications, such as word-of-mouth marketing and political campaigns. In particular, nodes with high structural importance may contribute negatively to the objective of the diffusion. To address this problem, we propose contextual centrality, which integrates structural positions, the diffusion process, and, most importantly, nodal contributions to the objective of the diffusion. We perform an empirical analysis of the adoption of microfinance in Indian villages and weather insurance in Chinese villages. Results show that contextual centrality of the first-informed individuals has higher predictive power towards the eventual adoption outcomes than other standard centrality measures. Interestingly, when the product of diffusion rate $p$ and the largest eigenvalue $\lambda_1$ is larger than one and diffusion period is long, contextual centrality linearly scales with eigenvector centrality. This approximation reveals that contextual centrality identifies scenarios where a higher diffusion rate of individuals may negatively influence the cascade payoff. Further simulations on the synthetic and real-world networks show that contextual centrality has the advantage of selecting an individual whose local neighborhood generates a high cascade payoff when $p \lambda_1 < 1$. Under this condition, stronger homophily leads to higher cascade payoff. Our results suggest that contextual centrality captures more complicated dynamics on networks and has significant implications for applications, such as information diffusion, viral marketing, and political campaigns

Topological resilience in non-normal networked systems

The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g. cascade failures in computer networks or parasitic species invasion in ecosystems. Understanding the networks topological features that affect the resilience phenomenon remains a challenging goal of the design of robust complex systems. We prove that the non-normality character of the network of interactions amplifies the response of the system to exogenous disturbances and can drastically change the global dynamics. We provide an illustrative application to ecology by proposing a mechanism to mute the Allee effect and eventually a new theory of patterns formation involving a single diffusing species