Complex Networks and their applications | 9am PT Tues, Apr 22, 2025

[Grigory Bronevetsky]

Modeling Talks

Complex Networks and their applications Guido Caldarelli, Ca' Foscari University of Venice Tues, April 22, 2025 | 9am PT Meet | Youtube Stream Hi all, The presentation will be via Meet and all questions will be addressed there. If you cannot attend live, the event will be recorded and can be found afterward at https://sites.google.com/modelingtalks.org/entry/complex-networks-and-their-applications More information on previous and future talks: https://sites.google.com/modelingtalks.org/entry/home Abstract: Complex systems are characterized by intricate interactions among their components, often leading to emergent behaviors that cannot be understood by studying individual parts in isolation. Network theory provides a powerful framework for analyzing such systems, representing components as nodes and their interactions as edges. In this talk, I will introduce key concepts in complex systems and network theory, including scale invariance, centrality measures, community detection, with a focus on applications to financial networks. I will discuss DebtRank, a network-based metric designed to quantify the systemic importance of financial institutions by considering not only their direct exposures but also the ripple effects of potential defaults. Unlike traditional risk measures, DebtRank captures the nonlinear propagation of distress through the network, offering regulators a more robust tool for identifying systemically risky entities. Bio: I am a statistical physicist with a degree in Condensed Matter Physics from Sapienza University of Rome and a PhD in the Theory of Condensed Matter from SISSA Trieste. After completing my PhD, I held various postdoctoral position in the UK, where I continue to collaborate with the London Institute for Mathematical Sciences. Currently, I serve as a Professor of Theoretical Physics at Ca’ Foscari University of Venice. In 2020, I was elected a Fellow of the American Physical Society (APS), and since 2024, I have been the Director of the Institute of Complex Systems at the National Research Council of Italy. My primary research focuses on the theory of complex networks and their applications to social systems.

[Grigory Bronevetsky]

Video Recording: https://youtube.com/live/9-CCoNS4Cls

Slides:

- pdf: https://drive.google.com/file/d/1OdMc2dV3IozloJzhP_DNQn4xXuLYWXb7/view?usp=sharing

- pptx: https://docs.google.com/presentation/d/17IFQbeS2KzlqLvX-fAFg5R2ZEae26LG-/edit?usp=sharing&ouid=110584304018462442605&rtpof=true&sd=true

Summary:

• Focus: modeling and analyzing complex systems

• Critical phenomena: critical points where system’s behavior transitions between major modes

• Theoretical framework: statistical physics

• Describes the distribution of masses of particles based on their statistical patterns of behavior

• Assumes homogeneity of behavior

• Not great at modeling social dynamics

• People are more complex than particles

• Fat tails: behavior is much more variable

• Current approach: describe meso-scopic behavior

• “Physics of humans”

• Using theoretical formalism of graph theory to model behavior

• Graphs

• Directed, undirected edges

• Can have labels/weights on nodes and edges

• Properties of social graphs:

• Scale invariant: very heterogeneous

• Small-world structures: travel easily across graphs

• E.g. on average it takes < 4 person-person connections on social networks to connect any person in the world to any other

• Very clusterized: many sub-communities

• Different ways to coarse-grain and summarize the graph

• Non-trivial centrality distributions

• Centrality metrics: degree, closeness, betweenness, eigenvector

• Applications for social dynamic analysis:

• Graph of marriage connections between different historical families

• Can identify hub families (Medici) and isolated ones (Pucci, strongest fighters)

• Graph of emails between academics (can see university structure) or phone call records (social structure)

• Can map the spread of lies on the Internet

• Politoscope:

• Tracking retweets of politicians to track spread of information

• Identifies political leanings of individuals and maps the political spectrum

• Analysis of financial networks

• Debtrank: https://www.nature.com/articles/srep00541

• Graph theoretic analysis of the financial ownership network

• Identifies ownership hubs (cross-ownership) and peripheries (owned by hubs)

• Financial institutions

• Assets: shares, interbank loans, household mortgages

• Liabilities: Deposits, bonds, household deposits, equity

• Shock on one sector (e.g. households) changes the asset/liability ratio

• Small shock: distress

• Big shock: bankruptcy

• Causes other companies to go into distress or bankruptcy

• Which propagates further through the ownership graph

• Leverage: investing using borrowed money

• Leverage ratio = total investment money / how much non-borrowed equity you have

• Leverage enables large-scale successful investments

• Amplifies both profits and losses for those investing with borrowed money

• Leverage connects lenders and borrowers: if borrowers’ investments fail, the loss propagates to the lender

• Model leverage relationships as a graph to track propagation of shocks through financial system

• Identify more central institutions that will be heavily impacted by shocks

• It's possible for the failure of some key entities to significantly affect the entire system

• Challenge: in reality the entire leverage/ownership graph is not known

• Need a way to estimate DebtRank from knowledge if pieces

• Approach: infer the most likely leverage graph by modeling as an exponential random graph and inferring