Systemic risk measured by the resiliency of the system to initial shocks.

The analysis of systemic risk often revolves around examining various measures utilized by practitioners and policymakers. These measures typically focus on assessing the extent to which external events can impact a financial system, without delving into the nature of the initial shock. In contrast, our approach takes a symmetrical standpoint and introduces a set of measures centered on the quantity of external shock that the system can absorb before experiencing deterioration.

Causal motifs and existence of endogenous cascades in directed networks with application to company defaults.

Motivated by the problem of detection of cascades of defaults in economy, we developed a detection framework for an endogenous spreading based on causal motifs we define in this paper. We assume that the change of state of a vertex can be triggered either by an endogenous (related to the network) or an exogenous (unrelated to the network) event, that the underlying network is directed and that times when vertices changed their states are available. After simulating default cascades driven by different stochastic processes on different synthetic networks, we show that some of the smallest causal motifs can robustly detect endogenous spreading events.

Controlling systemic risk: Network structures that minimize it and node properties to calculate it.

Evaluation of systemic risk in networks of financial institutions in general requires information of interinstitution financial exposures. In the framework of the DebtRank algorithm, we introduce an approximate method of systemic risk evaluation which requires only node properties, such as total assets and liabilities, as inputs. We demonstrate that this approximation captures a large portion of systemic risk measured by DebtRank.

Bi-stability of SUDR+K model of epidemics and test kits applied to COVID-19.

Motivated by the many diverse responses of different countries to the COVID-19 emergency, here we develop a toy model of the dependence of the epidemics spreading on the availability of tests for disease. Our model, that we call SUDR+K, grounds on the usual SIR model, with the difference of splitting the total fraction of infected individuals in two components: patients that are still undetected and patients that have been already detected through tests. Moreover, we assume that available tests increase at a constant rate from the beginning of epidemics but are consumed to detect infected individuals.

Color-avoiding percolation.

Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these vulnerabilities can greatly improve network robustness, if such paths exist.

Reduction of Systemic Risk by Means of Pigouvian Taxation.

We analyze the possibility of reduction of systemic risk in financial markets through Pigouvian taxation of financial institutions, which is used to support the rescue fund. We introduce the concept of the cascade risk with a clear operational definition as a subclass and a network related measure of the systemic risk. Using financial networks constructed from real Italian money market data and using realistic parameters, we show that the cascade risk can be substantially reduced by a small rate of taxation and by means of a simple strategy of the money transfer from the rescue fund to interbanking market subjects.

Extraction of temporal networks from term co-occurrences in online textual sources.

A stream of unstructured news can be a valuable source of hidden relations between different entities, such as financial institutions, countries, or persons. We present an approach to continuously collect online news, recognize relevant entities in them, and extract time-varying networks. The nodes of the network are the entities, and the links are their co-occurrences.

Geometric origin of scaling in large traffic networks.

Large scale traffic networks are an indispensable part of contemporary human mobility and international trade. Networks of airport travel and cargo ship movements are invaluable for the understanding of human mobility patterns [R. Guimera et al.

Topologically biased random walk and community finding in networks.

We present an approach of topology biased random walks for undirected networks. We focus on a one-parameter family of biases, and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion to study the features of random walks vs parameter values.

Hypergraph topological quantities for tagged social networks.

Recent years have witnessed the emergence of a new class of social networks, which require us to move beyond previously employed representations of complex graph structures. A notable example is that of the folksonomy, an online process where users collaboratively employ tags to resources to impart structure to an otherwise undifferentiated database. In a recent paper, we proposed a mathematical model that represents these structures as tripartite hypergraphs and defined basic topological quantities of interest.

Influence of reciprocal edges on degree distribution and degree correlations.

Reciprocal edges represent the lowest-order cycle possible to find in directed graphs without self-loops. Representing also a measure of feedback between vertices, it is interesting to understand how reciprocal edges influence other properties of complex networks. In this paper, we focus on the influence of reciprocal edges on vertex degree distribution and degree correlations.

Random hypergraphs and their applications.

In the last few years we have witnessed the emergence, primarily in online communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folksonomy, a tripartite structure of users, resources, and tags-labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures that represents them as random hypergraphs.

Reciprocity of networks with degree correlations and arbitrary degree sequences.

Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity r has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with arbitrary input and output degree sequences and given 2-node degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to r is revealed.