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.
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