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We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges between the clusters, as it is motivated by some earlier observations, e.g. in the structure of networks in ecology and economics and by applications of discrete tomography. Mathematically special colorings and chromatic numbers of graphs are studied., Comment: 15 pages, 3 figures, 1 table

We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the co-authorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Rand index and of the adjusted Wallace index respectively. The detection of cores is highly precise although the accuracy of the methodology can be limited in some cases., Comment: 9 pages, 6 figures

Recent studies uncovered important core/periphery network structures characterizing complex sets of cooperative and competitive interactions between network nodes, be they proteins, cells, species or humans. Better characterization of the structure, dynamics and function of core/periphery networks is a key step of our understanding cellular functions, species adaptation, social and market changes. Here we summarize the current knowledge of the structure and dynamics of "traditional" core/periphery networks, rich-clubs, nested, bow-tie and onion networks. Comparing core/periphery structures with network modules, we discriminate between global and local cores. The core/periphery network organization lies in the middle of several extreme properties, such as random/condensed structures, clique/star configurations, network symmetry/asymmetry, network assortativity/disassortativity, as well as network hierarchy/anti-hierarchy. These properties of high complexity together with the large degeneracy of core pathways ensuring cooperation and providing multiple options of network flow re-channelling greatly contribute to the high robustness of complex systems. Core processes enable a coordinated response to various stimuli, decrease noise, and evolve slowly. The integrative function of network cores is an important step in the development of a large variety of complex organisms and organizations. In addition to these important features and several decades of research interest, studies on core/periphery networks still have a number of unexplored areas., Comment: a comprehensive review of 41 pages, 2 figures, 1 table and 182 references