Using Minimum Spanning Trees to Analyze Equity Market Structure

Summary

This article explains how minimum spanning trees (MSTs) represent relationships among assets using a connected graph with minimal total edge weight. It describes visualizing trees with industry colors and market-cap node sizes, and reviews measures such as normalized tree length, shortest paths, degree connectivity, and betweenness centrality. These features can help researchers examine market structure, clustering, and possible risk transmission.

A case study compares trees for 48 stocks before, during, and after the COVID-related market decline. The reported tree length and average shortest path both fell during the decline, while the structure and central nodes changed; the authors interpret this as market-network shrinkage. A separate timing comparison using 183 stocks reports that Prim’s algorithm was faster in that experiment. These findings are descriptive and based on selected samples. The article cautions that MST clusters can change sharply with small input-data changes, so the network measures should not be treated as stable signals on their own.

Key ideas

• An MST condenses asset relationships into a connected graph with minimum total edge weight.
• Tree topology and measures such as normalized length and centrality can track changes in market structure.
• The examined stock network contracted during the COVID-related decline and did not fully return to its earlier configuration.
• The reported algorithm comparison favored Prim’s method for the tested larger dataset.
• MST clusters are sensitive to input data, which limits their reliability as standalone indicators.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.