**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31896

##### Interbank Networks and the Benefits of Using Multilayer Structures

**Authors:**
Danielle Sandler dos Passos,
Helder Coelho,
Flávia Mori Sarti

**Abstract:**

Complexity science seeks the understanding of systems adopting diverse theories from various areas. Network analysis has been gaining space and credibility, namely with the biological, social and economic systems. Significant part of the literature focuses only monolayer representations of connections among agents considering one level of their relationships, and excludes other levels of interactions, leading to simplistic results in network analysis. Therefore, this work aims to demonstrate the advantages of the use of multilayer networks for the representation and analysis of networks. For this, we analyzed an interbank network, composed of 42 banks, comparing the centrality measures of the agents (degree and PageRank) resulting from each method (monolayer *x* multilayer). This proved to be the most reliable and efficient the multilayer analysis for the study of the current networks and highlighted JP Morgan and Deutsche Bank as the most important banks of the analyzed network.

**Keywords:**
Complexity,
interbank networks,
multilayer networks,
network analysis.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.2576940

**References:**

[1] R.L. Flood, E. R. Carson, Dealing with complexity: an introduction to the theory and application of systems science, Springer Science & Business Media, 2013.

[2] D. Larsen-Freeman, “The emergence of complexity, fluency, and accuracy in the oral and written production of five Chinese learners of English,” Applied linguistics, vol. 27, 2006, pp. 590-619.

[3] M. Newman, Networks: an introduction, Oxford university press, 2010.

[4] E. Morin, La vía para el futuro de la humanidade, 2011.

[5] D. Braha, Unifying themes in complex systems. Y. Bar-Yam, A. Minai (Eds.), Westview Press, 2000.

[6] A. Ajzental, Complexidade aplicada à economia, Rio de Janeiro, RJ: Editora FGV, 2015.

[7] S. Bornholdt, H. G. Schuster (Eds.), Handbook of graphs and networks: from the genome to the internet, John Wiley & Sons, 2006.

[8] E. Cozzo, M. Kivelä, M. De Domenico, A. Solé-Ribalta, A. Arenas, S. Gómez, Y. Moreno, Structure of triadic relations in multiplex networks, in New Journal of Physics, vol. 17-ED 7, 2015, 073029.

[9] M. De Domenico, M. A. Porter, A. Arenas, MuxViz: a tool for multilayer analysis and visualization of networks, in Journal of Complex Networks, vol. 3-ED 2, 2015, pp. 159-176.

[10] M. De Domenico, A. Solé-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, M. Porter, S. Gómez, & A. Arenas, “Mathematical formulation of multilayer networks,” in Physical Review X, vol. 3-ED 4, 2013, 041022.

[11] M. Kivelä, A. Arenas, M. Barthelemy, J. P. Gleeson, Y. Moreno, M. A. Porter, “Multilayer networks,” in Journal of complex networks, vol. 2-ED 3, pp. 203-271, 2014.

[12] L. M. Verbrugge, “Multiplexity in adult friendships,” in Social Forces, vol. 57-ED 4, 1979, pp. 1286-1309.

[13] E. Lazega, M. T. Jourda, L. Mounier, R. Stofer, “Catching up with big fish in the big pond? Multi-level network analysis through linked design,” Social Networks, vol. 30, no. 2, pp. 159-176, 2008.

[14] D. Cai, Z. Shao, X. He, X. Yan, J. Han, (2005, October). “Community mining from multi-relational networks,” in European Conference on Principles of Data Mining and Knowledge Discovery, Berlin, 2005, pp. 445-452.

[15] S. Boccaletti, G. Bianconi, R. Criado, C. I. Del Genio, J. Gómez-Gardenes, M. Romance, M. Zanin, “The structure and dynamics of multilayer networks,” Physics Reports, vol. 544, pp. 1-122, 2014.

[16] I. Falih, & R. Kanawati, “MUMA: A multiplex network analysis library,” in Advances in Social Networks Analysis and Mining (ASONAM), 2015 IEEE/ACM International Conference on, pp. 757-760, Aug. 2015.

[17] M. De Domenico, C. Granell, M.A. Porter, A. Arenas, “The physics of spreading processes in multilayer networks,” Nature Physics, vol. 12-ED 10, pp. 901-906, 2016.

[18] H. Jeong, S. P. Mason, A.L. Barabási, Z. N. Oltvai, “Lethality and centrality in protein networks,” Nature, vol. 411, pp. 41-42, 2001.

[19] M. Boss, H. Elsinger, M. Summer, S. Thurner, “Network topology of the interbank market,” Quantitative Finance, vol. 4-ED 6, pp.677-684, 2004.

[20] H. Inaoka, H. Takayasu, T. Shimizu, T. Ninomiya, K. Taniguchi, “Self-similarity of banking network,” Physica A: Statistical Mechanics and its Applications, vol. 339-ED 3, pp. 621-634, 2004.

[21] K. Soramäki, M. L. Bech, J. Arnold, R. J. Glass, W. E. Beyeler, “The topology of interbank payment flows,” Physica A: Statistical Mechanics and its Applications, vol. 379, pp. 317-333, 2007.

[22] M. Montagna, C. Kok, “Multi-layered interbank model for assessing systemic risk,” unpublished.

[23] L. Euler, “Solutio problematis ad geometriam situs pertinentes,” Commentarii academiae scientiarum Petropolitanae, vol. 8, pp. 128-140, 1741.

[24] E. Nier, J. Yang, T. Yorulmazer, A. Alentorn, “Network models and financial stability,” Journal of Economic Dynamics and Control, vol. 31-ED 6, pp. 2033-2060, 2007.

[25] C. Upper, “Simulation methods to assess the danger of contagion in interbank markets,” Journal of Financial Stability, vol. 7-ED 3, pp. 111-125, 2011.

[26] S. Battiston, D. D. Gatti, M. Gallegati, B. Greenwald, J. E. Stiglitz, “Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk,” Journal of Economic Dynamics and Control, vol. 36-ED 8, pp. 1121-1141, 2012.

[27] B. M. Tabak, M. Takami, J. M. Rocha, D. O. Cajueiro, S. R. Souza, “Directed clustering coefficient as a measure of systemic risk in complex banking networks,” Physica A: Statistical Mechanics and its Applications, vol. 394, pp. 211-216, 2014.

[28] S. Poledna, J. L. Molina-Borboa, S. Martínez-Jaramillo, M. Van Der Leij, S. Thurner, “The multi-layer network nature of systemic risk and its implications for the costs of financial crises,” Journal of Financial Stability, vol. 20, pp. 70-81, 2015.

[29] M. Bardoscia, S. Battiston, F. Caccioli, G. Caldarelli, “Pathways towards instability in financial networks,” Nature Communications, vol. 8, pp. 14416, 2017.

[30] J. Nieminen, “On the centrality in a graph,” Scandinavian journal of psychology, vol. 15-ED 1, pp. 332-336, 1974.

[31] S. Brin, L. Page, “Reprint of: The anatomy of a large-scale hypertextual web search engine,” Computer networks, vol. 56-ED 18, pp. 3825-3833, 2012.

[32] A. Halu, R. J. Mondragón, P. Panzarasa, G. Bianconi, “Multiplex pagerank,” PloS one, vol. 8-ED 10, e78293, 2013.

[33] V. Grolmusz, “A note on the pagerank of undirected graphs,” arXiv preprint arXiv, pp. 1205.1960, 2012.