Abstract: We introduce a network valuation model (hereafter NEVA) for the ex-ante valuation of claims among financial institutions connected in a network of liabilities. Similar to previous work, the new framework allows to endogenously determine the recovery rate on all claims upon the default of some institutions. In addition, it also allows to account for ex-ante uncertainty on the asset values, in particular the one arising when the valuation is carried out at some time before the maturity of the claims. The framework encompasses as special cases both the ex-post approaches of Eisenberg and Noe and its previous extensions, as well as the ex-ante approaches, in the sense that each of these models can be recovered exactly for special values of the parameters. We characterize the existence and uniqueness of the solutions of the valuation problem under general conditions on how the value of each claim depends on the equity of the counterparty. Further, we define an algorithm to carry out the network valuation and we provide sufficient conditions for convergence to the maximal solution.

Abstract: In multi-layer networks with directed links, introducing measures of dependency between different layers requires more than a straightforward extension of the multiplexity measures that have been developed for undirected multiplexes. In particular, one should take into account the effects of reciprocity, i.e. the tendency of pairs of vertices to establish mutual connections. In single-layer networks, reciprocity is a crucial structural property affecting several dynamical processes. Here we extend it to multiplexes and introduce the notion of multireciprocity, defined as the tendency of links in one layer to be reciprocated by links in a different layer. While ordinary reciprocity reduces to a scalar quantity, multireciprocity requires a square matrix generated by all the possible pairs of layers.

Abstract: The Japanese banking crisis in the late 1990s has been considered a significant turning point in the history of the Japanese banking system. This period has attracted researchers' interest in studying the increase of bad debt on Japanese banks? balance sheets, which led to the crisis of the 1990s. Here we investigate the risk propagating through a bipartite banking network consisting of two kinds of nodes: assets on one hand and banks on the other. Using a Cascading Failure Model (CFM), originally proposed by Huang et al. [1], to describe the propagation of failures in the network, we attempt to understand the main culprit provoking the crisis and the systemic conditions that amplified or repressed the ?chain reaction? of bankruptcies

Abstract: Bipartite networks are currently regarded as providing a major insight into the organization of real-world systems, unveiling the mechanisms shaping the interactions occurring between distinct groups of nodes. One of the major problems encountered when dealing with bipartite networks is obtaining a (monopartite) projection over the layer of interest which preserves as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm to obtain statistically-validated monopartite projections of bipartite networks, which implements a entropy-based null-model We analyze a social network (i.e. the MovieLens dataset, a bipartite network of users and rated movies) and an economic network (i.e. the countries-products World Trade Web representation): while, in the first case, projecting Movie- Lens on the films layer allows clusters of movies belonging to similar genres to be detected, in the second case, projecting the World Trade Web on the countries layer reveals a modular structure of similarly-industrialized clusters of nations.

Abstract: We introduce two models of inclusion hierarchies: random graph hierarchy (RGH) and limited random graph hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erdos-Renyi random graph, with a fixed average degree equal to a system parameter c. Clusters of the resulting network are treated as nodes at the next hierarchy level and they are connected again at this level and so on, until the process cannot continue. In the RGH model we use all clusters, including those of size 1, when building the next hierarchy level, while in the LRGH model clusters of size 1 stop participating in further steps. We find that in both models the number of nodes at a given hierarchy level h decreases approximately exponentially with h. The height of the hierarchy H, i.e. the number of all hierarchy levels, increases logarithmically with the system size N, i.e. with the number of nodes at the first level. The height H decreases monotonically with the connectivity parameter c in the RGH model and it reaches a maximum for a certain c(max) in the LRGH model. The distribution of separate cluster sizes in the LRGH model is a power law with an exponent about -1.25. The above results follow from approximate analytical calculations and have been confirmed by numerical simulations.

Abstract: Information diffusion and epidemics outbreaks share a similar non linear dynamics which is studied in many scientific fields, including biology, engineering and physics.?The problem of controlling such types of dynamics in complex systems has recently been studied in different contexts. We shall provide an overview of recent? results obtained both in the case of control, i.e., when a central decision can be?operated and agents comply to the central controller, and strategic versions of the same?problems, where some of the agents may comply or not, or to a certain degree,? depending on their own utility, both in the case of cooperative behaviors and in the? case of competitive ones.?

Abstract: Worldwide firms interact with each other to form complex networks of financial relations. These financial interactions are partly captured by the ownership relations between them. We constructed the weighted and directed network of 800,000 companies forming multinational firms, with respect to their 1.2 million ownership relations (UNIL-GeoDivercity-Orbis, 2013) and extracted the corresponding directed network of the cities that harbor these firms. The firms, and therefore the cities, are then classified into five categories according to their main field of activity, i.e. high-tech, low-tech, knowledge-intensive services, low knowledge-intensive services and other (OECD, 2009). We employed this classification to divide the network into activity-specific relation networks that are connected through the cities they have in common, thus constructing a weighted and directed, multi-layered, partial-multiplex network of cities.