Disentangling bipartite and core-periphery structure in financial networks

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 characterizi...

Many networks can be usefully decomposed into a dense core plus an outlying, loosely-connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our method fits a generative model of core-periphery structure to observed data using a combination of an expectation--maximization algorithm for calculating the parameters of the model and a belief propagation algorithm for calculating the de...

Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank markets seem better characterised by a bipartite structure with more core-periphery connections than inside the core. Using a novel core-periphery detection metho...

Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it has been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The second is related to a large scale organization of the network, the core-periphery structure, composed by a dense core plus an outlying and loosely-connected periphery. In this paper we investigate the relation between these two concepts. ...

The framework of statistical inference has been successfully used to detect the meso-scale structures in complex networks, such as community structure, core-periphery (CP) structure. The main principle is that the stochastic block model (SBM) is used to fit the observed network and the learnt parameters indicate the group assignment, in which the parameters of model are often calculated via an expectation-maximization (EM) algorithm and a belief propagation (BP) algorithm is ...

Core-periphery structure, the arrangement of a network into a dense core and sparse periphery, is a versatile descriptor of various social, biological, and technological networks. In practice, different core-periphery algorithms are often applied interchangeably, despite the fact that they can yield inconsistent descriptions of core-periphery structure. For example, two of the most widely used algorithms, the k-cores decomposition and the classic two-block model of Borgatti a...

The topological properties of interbank networks have been discussed widely in the literature mainly because of their relevance for systemic risk. Here we propose to use the Stochastic Block Model to investigate and perform a model selection among several possible two block organizations of the network: these include bipartite, core-periphery, and modular structures. We apply our method to the e-MID interbank market in the period 2010-2014 and we show that in normal condition...

While studies of meso-scale structures in networks often focus on community structure, core--periphery structures can reveal new insights. This structure typically consists of a well-connected core and a periphery that is well connected to the core but sparsely connected internally. Most studies of core--periphery structure focus on undirected networks. We propose a generalisation of core-periphery structure to directed networks. Our approach yields a family of core-periphe...

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via incre...

Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific disciplines, it has not received sufficient attention in the statistics community. In this expository article, our goal is to raise awareness about this topic and encourage statisticians to address the many open inference problems in this area. To this end, ...