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Structural patterns in complex systems using multidendrograms

Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural properties. The finding of structural patterns is of utmost importance to reduce the problem of understanding the structure-function relationships. Here we propose the analysis of similarity measures between nodes using hierarchical clustering methods. The discrete nature of the networks usually leads to a small set of different similarity values, making standard hierarchical clustering algorithms ambiguous. We propose the use of "multidendrograms", an algorithm that computes agglomerative hierarchical clusterings implementing a variable-group technique that solves the non-uniqueness problem found in the standard pair-group algorithm. This problem arises when there are more than two clusters separated by the same maximum similarity (or minimum distance) during the agglomerative process. Forcing binary trees in this case means breaking ties in some way, thus giving rise to different output clusterings depending on the criterion used. Multidendrograms solves this problem grouping more than two clusters at the same time when ties occur.