Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both unweighted and weighted scale free networks having local and global core-periphery as well as community structure. Network evolves using topological growth, self growth, and weight distribution function. To validate the correctness of proposed models, we use K-shell and S-shell decomposition methods. Simulation results show that the generated unweighted networks follow power law degree distribution with droop head and heavy tail. Similarly, generated weighted networks follow degree, strength, and edge-weight power law distributions. We further study other properties of complex networks, such as clustering coefficient, nearest neighbor degree, and strength degree correlation.
Complex networks have gained more attention from the last few years. The size of the real world complex networks, such as online social networks, WWW networks, collaboration networks, is exponentially increasing with time. It is not feasible to completely collect, store and process these networks. In the present work, we propose a method to estimate the degree centrality ranking of a node without having complete structure of the graph. The proposed algorithm uses degree of a node and power law exponent of the degree distribution to calculate the ranking. We also study simulation results on Barabasi-Albert model. Simulation results show that the average error in the estimated ranking is approximately 5% of the total number of nodes.
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