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.
A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia Received 28 January 2000!We study the growth of a network with aging of sites. Each new site of the network is connected to some oldsite with probability proportional i! to the connectivity of the old site as in the Baraba´si-Albert’s model and ii! to t A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) approximately k(gamma), different behaviors arise for gamma 1, and gamma = 1. For gamma 1, a single site connects to nearly all other sites. In the borderline case A(k) approximately k, the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2<nu<infinity. Motivated by data on the evolution of the Internet and World Wide Web we consider scenarios of self-organization of the nonlinearly growing networks into free-scale structures. We find that the accelerating growth of the networks establishes their structure. For the growing networks with preferential linking and increasing density of links, two scenarios are possible. In one of them, the value of the exponent @math of the connectivity distribution is between 3 2 and 2. In the other, @math and the distribution is necessarily non-stationary.