A tool for filtering information in complex systems

2005/01/31 by Michele Tumminello, M. Tumminello, Tomaso Aste +5 · 918 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Biology #Combinatorics #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Computer science #Filter (signal processing) #Genus #Graph #Mathematics #Opinion Dynamics and Social Influence #Planar #Spanning tree #Theoretical computer science #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph

paper · pdf · doi:10.1073/pnas.0500298102

published in Proceedings of the National Academy of Sciences 102(30), 10421-10426 (National Academy of Sciences) · 8 pages, 3 figures, 4 tables

openalex publication_date 2005/07/18 · arxiv created 2005/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 that 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 four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.

Citations

• Evolution of networks

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