A tool for filtering information in complex systems

TL;DR

This paper presents a graph filtering technique that simplifies complex data-sets by controlling the graph's genus, effectively preserving hierarchical structures and revealing significant market relationships.

Contribution

The authors introduce a tunable graph filtering method based on genus control, enhancing the analysis of correlation-based graphs in complex systems.

Findings

Filtered graphs preserve hierarchical organization

Planar filtered graphs contain meaningful loops and cliques

Application to stock data reveals significant market structures

Abstract

We introduce a technique to filter out complex data-sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation based graphs giving filtered graphs which preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0) triangular loops and 4 element cliques are formed. The application of this filtering procedure to 100 stocks in the USA equity markets shows that such loops and cliques have important and significant relations with the market structure and properties.