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'''Financial networks''' are the network structures formed by financial institutions, markets, and instruments through which capital, risk, and information flow. They include banking networks, payment systems, derivatives markets, and the [[Shadow Banking|shadow banking]] system. The study of financial networks applies tools from [[Network Theory|network theory]], [[Graph Theory|graph theory]], and [[Complex Adaptive Systems|complex adaptive systems]] to understand how the structure of financial relationships determines the stability and fragility of the financial system.

The defining feature of financial networks is that they are '''adaptive''': the network topology changes in response to market conditions, regulation, and the strategic behavior of the institutions that form the network's nodes. When a financial institution fails, other institutions change their lending relationships, altering the network topology. When regulation changes, institutions restructure their operations, rewiring the network. The financial network is therefore not a static graph but a '''co-evolving system''' in which the nodes and edges adapt to each other's states.

Financial networks exhibit the classic properties of [[Scale-Free Networks|scale-free networks]]: a small number of major institutions — global systemically important banks (G-SIBs) — act as hubs with thousands of connections, while the vast majority of institutions have few connections. This hub structure creates a '''robust-yet-fragile''' property: the network is robust to the random failure of small institutions but catastrophically vulnerable to the failure of a hub. The 2008 financial crisis demonstrated this property when the failure of Lehman Brothers — a hub in the investment banking network — triggered a global financial panic.

The study of financial networks has revealed several mechanisms of [[Systemic Risk|systemic risk]]:

* '''Direct contagion''': The failure of one institution causes direct losses to its creditors, who may then fail. This is the mechanism of a [[Bank run|bank run]]: depositors withdraw funds because they fear other depositors will withdraw, creating a self-fulfilling prophecy.

* '''Indirect contagion''': The failure of one institution causes asset fire sales that depress prices, causing losses to institutions that hold similar assets but were not directly connected to the failed institution. This is the mechanism of the [[2008 financial crisis|2008 crisis]]: the collapse of the subprime mortgage market caused losses to institutions that had never made a subprime loan.

* '''Feedback amplification''': Distress in one part of the network triggers margin calls and collateral demands that force asset sales, which depress prices, which trigger further margin calls. This is the mechanism of the [[Credit Default Swap|CDS]] collateral spiral: a local credit deterioration is amplified into a global asset fire sale by the network's feedback loops.

Financial networks are also characterized by '''layered complexity''': the visible layer of regulated banking relationships is coupled to an invisible layer of [[Over-the-counter|over-the-counter]] derivatives, repo markets, and shadow banking entities. The two layers are connected through cross-exposures: a regulated bank may lend to a shadow bank, which uses the loan to buy derivatives from another regulated bank. The coupling between layers means that distress in the invisible layer can propagate to the visible layer through channels that regulators do not monitor.

The policy implications of financial network research are structural. Traditional macroprudential regulation — capital requirements, liquidity ratios, stress tests — addresses the properties of individual institutions without considering the network structure that connects them. A systemically important institution may be well-capitalized individually but systemically fragile because of its position in the network. Effective regulation must therefore target '''network properties''': concentration ratios, centrality measures, and contagion thresholds, not just individual balance sheets.

The study of financial networks is part of a broader convergence between economics and physics. The tools of [[Statistical mechanics|statistical mechanics]], [[Percolation theory|percolation theory]], and [[Renormalization Group|renormalization group]] theory are being applied to financial systems with increasing sophistication. The goal is not merely to predict crises but to understand the '''phase transitions''' that financial networks undergo — the abrupt shifts from stable to unstable states that characterize systems near critical points. The financial network, like the [[Ising model|Ising model]] or the [[Bak-Tang-Wiesenfeld model|sandpile model]], may be a physical system in the guise of a social institution.

[[Category:Economics]]
[[Category:Network Theory]]
[[Category:Systems]]
[[Category:Complexity]]