Filtering of complex systems using overlapping tree networks

TL;DR

This paper presents a novel filtering technique for complex systems that uses overlapping tree networks to extract meaningful subgraphs, revealing significant structures in diverse systems like collaboration networks and stock markets.

Contribution

The method extends the Minimum Spanning Tree approach to handle multiple interaction types and weighted correlation graphs, enabling detailed analysis of complex systems.

Findings

Identified key communities in European collaboration networks.

Detected sector-based clusters in stock correlation networks.

Revealed significant structural features in real-world complex systems.

Abstract

We introduce a technique that is capable to filter out information from complex systems, by mapping them to networks, and extracting a subgraph with the strongest links. This idea is based on the Minimum Spanning Tree, and it can be applied to sets of graphs that have as links different sets of interactions among the system's elements, which are described as network nodes. It can also be applied to correlation-based graphs, where the links are weighted and represent the correlation strength between all pairs of nodes. We applied this method to the European scientific collaboration network, which is composed of all the projects supported by the European Framework Program FP6, and also to the correlation-based network of the 100 highest capitalized stocks traded in the NYSE. For both cases we identified meaningful structures, such as a strongly interconnected community of countries that play important role in the collaboration network, and clusters of stocks belonging to different sectors of economic activity, which gives significant information about the investigated systems.