Coincidence complex networks

Complex networks, which constitute the main subject of network science, have been wide and extensively adopted for representing, characterizing, and modeling an ample range of structures and phenomena from both theoretical and applied perspectives. The present work describes the application of the real-valued Jaccard and real-valued coincidence similarity indices for translating generic datasets into networks. More specifically, two data elements are linked whenever the similarity between their respective features, gauged by some similarity index, is greater than a given threshold. Weighted networks can also be obtained by taking these indices as weights. It is shown that the two proposed real-valued approaches can lead to enhanced performance when compared to cosine and Pearson correlation approaches, yielding a detailed description of the specific patterns of connectivity between the nodes, with enhanced modularity. In addition, a parameter α is introduced that can be used to control the contribution of positive and negative joint variations between the considered features, catering for enhanced flexibility while obtaining networks. The ability of the proposed methodology to capture detailed interconnections and emphasize the modular structure of networks is illustrated and quantified respectively to real-world networks, including handwritten letters and raisin datasets, as well as the Caenorhabditis elegans neuronal network. The reported methodology and results pave the way to a significant number of theoretical and applied developments.