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In this article, we present various algorithms to partition the nodes of a network into groups that show the property of nestedness. Since perfect nestedness is a rare phenomenon, we consider the task from a data mining perspective, and we search for groups having high-level of nestedness. We utilize both agglomerative and divisive hierarchical clustering procedures and compare them on several benchmark and real-life networks. Furthermore, we propose different metrics derived from the results of our algorithms. We show that average-linkage and complete-linkage clustering can recover the largest fully nested clusters, and that the cluster size-weighted mean nestedness was a more stable metric for measuring clustering performance. Our proposed algorithms allow us to create multiple resolution views of nestedness-based clustering of networks, extending the field of graph-based data mining. [ABSTRACT FROM AUTHOR]

In this study, a mathematical model is presented for an online data clustering problem. Data clustering plays an important role in many applications like handling the data acknowledgment problem and data stream management in real-time locating systems. The inputs in these problems are data sequences, each containing several data elements. Each data element has an arrival time and a weight that reflects its importance. The arrival times are not known in advance, and some data elements never arrive. Hence the system should decide which moment is optimal for forwarding the collected data for processing. This requires finding a good trade-off between the amount of collected information and the waiting time, which may be regarded as a minimization problem. Here, we investigate several online algorithms and present their competitive analysis and average case studies. Experimental results, based on simulations using artificially generated data, are also presented and they confirm the efficiency of our methods.

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 the key step to our understanding of 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. By 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. [ABSTRACT FROM AUTHOR]