SPECTRAL TOPOLOGY OF GLOBAL IMBALANCES: A GRAPH-THEORETIC FRAMEWORK FOR SYSTEMIC RISK IN THE BALANCE OF PAYMENTS
DOI:
https://doi.org/10.63456/aamc-2-1-87Keywords:
Balance of payments, exposure networks, spectral stability, systemic risk, directed Laplacian, non-backtracking thresholdAbstract
We model global balance-of-payments linkages as a directed weighted exposure network and study systemic fragility through the spectrum of the associated operators. From a signed bilateral-flow matrix we construct a nonnegative exposure lift, derive a spectral stability criterion for linear propagation, and define node- and edge-level risk measures using Perron–Frobenius geometry, PageRank, and marginal spectral impact. We further give two complementary extensions: a directed Laplacian formulation for shock diffusion and a non-backtracking threshold for cascade formation on sparse exposure networks. The framework identifies systemic risk as a topological property of the global network, rather than a collection of isolated country indicators, and yields mathematically explicit diagnostics for resilience, concentration of stress, and targeted stabilization.
References
[1] International Monetary Fund, Balance of Payments and International Investment Position Manual,
Sixth Edition (BPM6), IMF, Washington, DC, 2009.
[2] S. Brin and L. Page, The anatomy of a large-scale hypertextual web search engine, Computer
Networks, 30 (1998), 107–117.
[3] F. Chung, Laplacians and the Cheeger inequality for directed graphs, Annals of Combinatorics 9
(2005), 1–19.
[4] B. Karrer, M. E. J. Newman, and L. Zdeborov´a, Percolation on sparse networks, Physical Review
Letters 113 (2014), 208702.
[5] B. Karrer, M. E. J. Newman, and L. Zdeborov´a, Percolation on sparse networks, arXiv:1405.0483
(2014).
[6] J. Martin, Percolation and localization: sub-leading eigenvalues of the non-backtracking matrix on
directed networks, Journal of Complex Networks (2025).
[7] G. Fagiolo, J. Reyes, and S. Schiavo, The evolution of the world trade web: a weighted-network
analysis, Journal of Evolutionary Economics 20 (2010), 479–514.
[8] M. Due˜nas, G. Fagiolo, and S. Schiavo, Global trade imbalances: a network approach, (Working
paper version, 2013).
14
[9] S. M. Markose, Systemic Risk from Global Financial Derivatives: A Network Analysis of Contagion
and Its Mitigation with Super-Spreader Tax, IMF Working Paper WP/12/282, 2012.
[10] R. Triffin, Gold and the Dollar Crisis: The Future of Convertibility (and related exposition),
Princeton IES PDF (archival), 1960/1961 era.
[11] E. Seneta, Non-negative Matrices and Markov Chains, Springer, 2006.
[12] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM Classics
in Applied Mathematics, 1994.
[13] R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed., Cambridge University Press, Cambridge,
2012.
[14] G. W. Stewart and J.-g. Sun, Matrix Perturbation Theory, Academic Press, Boston, 1990.
[15] T. Kato, Perturbation Theory for Linear Operators, Classics in Mathematics, Springer, Berlin,
1995. doi: 10.1007/978-3-642-66282-9.
[16] R. S. Varga, Matrix Iterative Analysis, 2nd ed., Springer Series in Computational Mathematics,
Springer, Berlin, 2000. doi: 10.1007/978-3-642-05156-2.
[17] L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications, Wiley-Interscience,
New York, 2000.
[18] L. Katz, A new status index derived from sociometric analysis, Psychometrika 18 (1953), no. 1,
39–43. doi: 10.1007/BF02289026.
[19] P. Bonacich, Power and centrality: A family of measures, American Journal of Sociology 92 (1987),
no. 5, 1170–1182. doi: 10.1086/228631.
[20] M. Scheffer, J. Bascompte, W. A. Brock, V. Brovkin, S. R. Carpenter, V. Dakos, H. Held, E. H.
van Nes, M. Rietkerk, and G. Sugihara, Early-warning signals for critical transitions, Nature 461
(2009), no. 7260, 53–59. doi: 10.1038/nature08227.
[21] A. N. Langville and C. D. Meyer, Google’s PageRank and Beyond: The Science of Search Engine
Rankings, Princeton University Press, Princeton, NJ, 2006.
[22] D. Acemoglu, A. Ozdaglar, and A. Tahbaz-Salehi, Systemic risk and stability in financial networks,
American Economic Review 105 (2015), no. 2, 564–608. doi: 10.1257/aer.20130456.
[23] M. Elliott, B. Golub, and M. O. Jackson, Financial networks and contagion, American Economic
Review 104 (2014), no. 10, 3115–3153. doi: 10.1257/aer.104.10.3115.
[24] P. Glasserman and H. P. Young, Contagion in financial networks, Journal of Economic Literature
54 (2016), no. 3, 779–831. doi: 10.1257/jel.20151243.
[25] S. Battiston, M. Puliga, R. Kaushik, P. Tasca, and G. Caldarelli, DebtRank: Too central to
fail? Financial networks, the FED and systemic risk, Scientific Reports 2 (2012), 541. doi:
10.1038/srep00541.
[26] F. R. K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, Vol. 92,
American Mathematical Society, Providence, RI, 1997. ISBN: 0821803158.
[27] D. A. Levin and Y. Peres, with contributions by E. L. Wilmer, Markov Chains and Mixing Times,
2nd ed., American Mathematical Society, Providence, RI, 2017. doi:10.1090/mbk/107.
[28] L. Lov´asz, Random walks on graphs: A survey, in Combinatorics, Paul Erd˝os is Eighty, Vol. 2,
Bolyai Society Mathematical Studies, 1993, pp. 1–46.
[29] B. Karrer, M. E. J. Newman, and L. Zdeborov´a, Percolation on sparse networks, Phys. Rev. Lett.
113 (2014), 208702.
[30] M. E. J. Newman, Message passing methods on complex networks, arXiv:2211.05054 (2022).
15
[31] K.-I. Hashimoto, Zeta functions of finite graphs and representations of p-adic groups, in Automor-
phic Forms and Geometry of Arithmetic Varieties, Advanced Studies in Pure Mathematics, Vol. 15,
(1989), 211–280.
[32] J. Martin, L. Zanetti, and T. Rogers, Percolation and localization: sub-leading eigenval-
ues of the nonbacktracking matrix, Journal of Complex Networks 13(5) (2025), cnaf027.
doi:10.1093/comnet/cnaf027.
[33] J. G. Restrepo, E. Ott, and B. R. Hunt, Weighted percolation on directed networks, arXiv:0704.0491
(2007).
[34] D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed., Taylor & Francis, London,
1994.
[35] R. Triffin, Gold and the Dollar Crisis: The Future of Convertibility, Yale University Press, New
Haven, 1960.
[36] E. Farhi and M. Maggiori, A Model of the International Monetary System, The Quarterly Journal
of Economics 133(1) (2018), 295–355. doi:10.1093/qje/qjx031.
[37] G. Gopinath, E. Boz, C. Casas, F. J. D´ıez, P.-O. Gourinchas, and M. Plagborg-
Møller, Dominant Currency Paradigm, American Economic Review 110(3) (2020), 677–719.
doi:10.1257/aer.20171201.
[38] G. Adler et al., Dominant Currencies and External Adjustment, IMF Staff Discussion Note
No. SDN/20/05, International Monetary Fund, July 2020.
[39] Bank for International Settlements, Global liquidity indicators: background and interpretation,
BIS Quarterly Review, March 2015 (information box, 18 March 2015).
[40] P.-O. Gourinchas and H. Rey, From World Banker to World Venture Capitalist: U.S. External
Adjustment and the Exorbitant Privilege, NBER Working Paper No. 11563, 2005.
[41] P.-O. Gourinchas and H. Rey, From World Banker to World Venture Capitalist: U.S. External
Adjustment and the Exorbitant Privilege, in G7 Current Account Imbalances: Sustainability and
Adjustment, R. H. Clarida (ed.), University of Chicago Press, 2007, pp. 11–66.
[42] R. Nurkse, International Currency Experience: Lessons of the Inter-War Period, League of Nations,
Economic, Financial and Transit Department, 1944.
[43] J. M. Keynes, Proposals for an International Clearing Union, White Paper, Cmd. 6437, H. M.
Stationery Office, London, April 1943.
[44] A. G. Haldane and R. M. May, Systemic risk in banking ecosystems, Nature 469 (2011), 351–355.
doi:10.1038/nature09659.
[45] Y.-Y. Liu, J.-J. Slotine, and A.-L. Barab´asi, Controllability of complex networks, Nature 473
(2011), 167–173. doi:10.1038/nature10011.
[46] International Monetary Fund, International Trade in Goods (by partner country) (IMTS) (formerly
Direction of Trade Statistics, DOTS), IMF Data. Accessed 03 Jan 2026. https://data.imf.org/
en/datasets/IMF.STA:IMTS
[47] United Nations Statistics Division, UN Comtrade Database, United Nations. Accessed 03 Jan 2026.
[48] International Monetary Fund, Portfolio Investment Positions by Counterpart Economy (PIP)
(formerly Coordinated Portfolio Investment Survey, CPIS), IMF Data. Accessed 03 Jan 2026.
https://data.imf.org/en/datasets/IMF.STA:PIP
[49] International Monetary Fund, Balance of Payments (BOP), IMF Data. Accessed 03 Jan 2026.
https://data.imf.org/en/datasets/IMF.STA:BOP
16
[50] International Monetary Fund, International Investment Position (IIP), IMF Data. Accessed 03
Jan 2026. https://data.imf.org/Datasets/IIP
[51] Bank for International Settlements, Locational banking statistics (LBS): overview, BIS Data Portal.
Accessed 03 Jan 2026. https://www.bis.org/statistics/bankstats.htm
[52] Bank for International Settlements, Consolidated banking statistics (CBS): overview, BIS Data
Portal. Accessed 03 Jan 2026. https://www.bis.org/statistics/consstats.htm
[53] M. Marini, R. Dippelsman, and M. Stanger, New Estimates for Direction of Trade Statis-
tics, IMF Working Paper WP/18/16, January 2018. https://www.imf.org/-/media/files/
publications/wp/2018/wp1816.pdf
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Copyright (c) 2026 Chandrasekhar Gokavarapu, Sanjeev Kumar Chejarla, Balayya Rajana, V. N. S. R. Murthy Duggirala, Srinivasulu Chittaru (Author)
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