Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barab\'asi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks

Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling, after an introduction to the main concepts and models. A diversity of phenomena are surveyed, which may be classified into no less than 22 areas, providing a clear indication of the impact of the field of complex networks.Comment: 103 pages, 3 figures and 7 tables. A working manuscript, suggestions are welcome