Parameter-free identification of salient features in complex networks

Details Parameter-free identification of salient features in complex networks Parameter-free identification of salient features in complex networks

2011-10-18

arxiv.org/abs/1110.3864v2

Physics

Physics and Society

Scientific paper

Large scale complex networks in natural, social, and technological systems generically exhibit an overabundance of rich information. Extracting essential and meaningful structural features from network data is one of the most challenging tasks in network theory. In this context, a variety of methods and concepts have been proposed, including centrality statistics, motif identification, community detection algorithms, hierarchical models, and backbone-extraction methods. Typically these classification schemes rely on external and often arbitrary parameters, such as centrality thresholds. However, parameter-dependent classifications are often problematic, since the resulting classifications of network elements depend sensitively on the parameter, and it is also unknown whether typical networks permit the classification of elements without external intervention. Here we introduce the concept of link salience, a parameter-free approach for classifying network elements based on a consensus estimate of all nodes. We show that a wide range of empirical networks exhibit a natural, network-implicit, and robust classification of links into two qualitatively distinct groups. We show that despite significant differences in the networks' topology and statistical features, their salient skeletons exhibit universal topological and statistical features. In addition to a parameter- free method for network reduction, link salience points the way towards a better understanding of universal, hidden features in real world networks that are masked by their complexity.

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