### Discussion Paper

## Abstract

In this paper the authors focus on credit connections as a potential source of systemic risk. In particular, they seek to answer the following question: how do we find densely connected subsets of nodes within a credit network? The question is relevant for policy, since these subsets are likely to channel any shock affecting the network. As it turns out, a reliable answer can be obtained with the aid of complex network theory. In particular, the authors show how it is possible to take advantage of the ‘community detection’ network literature. The proposed answer entails two subsequent steps. Firstly, the authors need to verify the hypothesis that the network under study truly has communities. Secondly, they need to devise a reliable algorithm to find those communities. In order to be sure that a given algorithm works, they need to test it over a sample of random benchmark networks with known communities. To overcome the limitation of existing benchmarks, the authors introduce a new model and test alternative algorithms, obtaining very good results with an adapted spectral decomposition method. To illustrate this method they provide a community description of the Japanese bank-firm credit network, getting evidence of a strengthening of communities over time and finding support for the well-known Japanese ‘main bank’ system. Thus, the authors find comfort both from simulations and from real data on the possibility to apply community detection methods to credit markets. They believe that this method can fruitfully complement the study of contagious defaults, since the likelihood of intracommunity default contagion is expected to be high.

Paper submitted to the special issue Coping with Systemic Risk

## Comments and Questions

Identifying communities in financial networks is both important and difficult. It is important as contagion within communities is likely to be more severe, and if these communities are important the effects may spill over to other communities. In large networks it often makes sense to talk about systemically important communities ...[more]

... rather than systemically important banks.

The paper reviews literature on building artificial networks with community structures and extends methodologies for ensuring that a community detection algorithm indeed identifies communities that are known to exist in a network. The authors then test two algorithms for their ability to detect communities in network ensembles generated on the basis of a Modular Binomial Model introduced in the paper. They find that an adaptation of Donetti and Munoz (2005) based on spectral decomposition provides best results. Finally the authors apply the method on bipartite bank-firm credit networks in the Japanese economy and find that the communities are relatively small (up to ~80) The algorithm is also able to detect small communities improving on 'resolution bias' present in main existing algorithms.

The paper presents new methodologies for community detection that are likely to find many applications in addition to the one presented by the authors. The paper is, however, very technical and at times hard to follow.

For clarity of exposition, please spell out:

- that F and B represent firms and banks (when introduced on page 4)

- left hand side elements for Equation 2.1

- small delta in Eq. 2.2 vs Eq. 3.1 and 3.3 (if they are the same, use same notation and introduce delta in 2.2)

- that ME stands for Maximum Entropy -model (when abbreviation is introduced on page 7) and MB for Modular Binomial (when abbreviation is introduced on page 9)

- s in Eq. 3.1.

- spell out x-axis in all figures

In general redundancy on using both verbal explanations and mathematical notation for the many variables would make the paper easier to read.

On a substance note:

- A few words on the relationship between systemic risk and communities would be beneficial - i.e. that contagion can magnify within a community and spill over to other communities. Therefore it is important to identify the systemically important communities in addition to systemically important banks. The same way as we need to know which banks are in the system to evaluate who are important, we need to identify first communities before evaluating which ones are important.

- Bonferroni correction may be too conservative for large matrices (211x211). A false discovery rate approach could be more suitable.

- There is quite a wide literature on the statistical properties (including clusters and communities) of empirical financial networks:

Boss et al 2004 - http://eco83.econ.unito.it/~dottorato/03-10-054.pdf

Soramaki et al 2007 - http://www.sciencedirect.com/science/article/pii/S0378437106013124

Craig and von Peter 2010 - http://www.bis.org/publ/work322.pdf

This relevant literature is largely missed by the paper.