Glossary

Graph Theory

Graph theory is the mathematical study of networks composed of nodes (vertices) and edges (links). In econometrics and financial risk, graph-theoretic tools underpin network analysis of connectedness — for example, mapping how volatility shocks propagate across firms or markets.

Definition

Why It Matters

Modern financial systems are deeply interconnected, and graph theory provides the vocabulary and toolkit to model these connections rigorously. By representing institutions as nodes and their relationships as edges, researchers can identify systemically important players, measure contagion risk, and detect community structure in markets. Variance decomposition networks from VAR models, minimum spanning trees of correlation matrices, and centrality measures (degree, betweenness, eigenvector) all rely on graph-theoretic foundations. Without graph theory, analysts would lack a principled way to summarise and visualise the complex web of linkages that drive systemic risk.

Example

A financial regulator constructs a volatility spillover network among 20 major banks using forecast-error variance decomposition. The resulting directed graph reveals that Bank A has the highest out-degree centrality, meaning its shocks transmit to the most other banks. This identifies Bank A as a systemically important institution warranting closer supervisory attention and higher capital requirements.

Related Terms

Software Notes

SPSS: Limited native support; use the Network Analyst extension or export edge lists for external tools
R: igraph package for constructing and analysing graphs; network and sna packages for social network analysis; qgraph for visualisation
Stata: nwcommands suite for network construction and analysis; netplot for visualisation