Flow Decomposition in Complex Systems

Complex systems can be represented as weighted digraphs. Cycles play an important role in complex systems because they define relationships consisting of unique groupings of nodes. A grouping of connected nodes contains rich contextual meaning because of the relationships defined by its connecting edges. Cycle bases are a description of the set of all independent cycles within a graph. The work herein outlines a computational methodology to decompose the total through flow of a complex system into a set of coefficients over its cycle bases. A coefficient is computed for each cycle representing the cycle´scontribution to the total system through flow. This vector of coefficients provides information for data mining and information clustering applications to analyze the system. The proposed methodology provides a powerful framework for analyzing symbolic data by assigning magnitude values to the contextual meaning within groupings of symbols.