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.
In traffic networks, when a new node connects to an existing node, it increases traffic on that node. This increased traffic is distributed across all neighbors of the node. Such a distribution is called local rearrangement of the weights. In 2004, A @cite_20 studied this approach and proposed a weighted evolving model, that is also called BBV (Barrat, Barthelemy, and Vespignani) model. @cite_40 @cite_30 proposed traffic driven weighted models, where edge weights can be calculated using traffic flow or betweenness centrality measure.
@cite_30 @cite_40 @cite_20
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We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges’ weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights’ reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several realworld systems. In particular, the model yields a nontrivial time evolution of vertices’ properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices’ degree. Most of existing works on complex network assumed that the nodes and edges were uncapacitated during the evolving process, and displayed “rich club” phenomenon. Here we will show that the “rich club” could be changed to “common rich” if we consider the node capacity. In this paper, we define the node and edge attractive index with node capacity, and propose a new evolving model on the base of BBV model, with evolving simulations of the networks. In the new model, an entering node is linked with an existing node according to the preferential attachment mechanism defined with the attractive index of the existing node. We give the theoretical approximation and simulation solutions. If node capacity is finite, the rich node may not be richer further when the node strength approaches or gets to the node capacity. This is confirmed by analyzing the passenger traffic and routes of Chinese main airports. Due to node strength being function of time t, we can use the theoretical approximation solution to forecast how node strength changes and the time when node strength reaches its maximum value. We are witnessing increasing interests in the effective use of road networks. For example, to enable effective vehicle routing, weighted-graph models of transportation networks are used, where the weight of an edge captures some cost associated with traversing the edge, e.g., greenhouse gas (GHG) emissions or travel time. It is a precondition to using a graph model for routing that all edges have weights. Weights that capture travel times and GHG emissions can be extracted from GPS trajectory data collected from the network. However, GPS trajectory data typically lack the coverage needed to assign weights to all edges. This paper formulates and addresses the problem of annotating all edges in a road network with travel cost based weights from a set of trips in the network that cover only a small fraction of the edges, each with an associated ground-truth travel cost. A general framework is proposed to solve the problem. Specifically, the problem is modeled as a regression problem and solved by minimizing a judiciously designed objective function that takes into account the topology of the road network. In particular, the use of weighted PageRank values of edges is explored for assigning appropriate weights to all edges, and the property of directional adjacency of edges is also taken into account to assign weights. Empirical studies with weights capturing travel time and GHG emissions on two road networks (Skagen, Denmark, and North Jutland, Denmark) offer insight into the design properties of the proposed techniques and offer evidence that the techniques are effective. Many social, technological, biological and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most existing research work on complex network models are concentrated on network structures, with connection weights among their nodes being either 1 or 0. In this paper, we propose a new weighted evolving network model. Numerical simulations indicate that this network model yields three power-law distributions for the node degrees, connection weights and node strengths, respectively. Particularly, some other properties of the distributions, such as the droop-head and heavy-tail effects, can also be reflected by this model.