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 2001, Bianconi and Barabasi @cite_0 proposed a modeling phenomenon, where probability of connection is directly proportional to the fitness value of a node. There are some more models based on different properties of nodes, such as intrinsic strength @cite_43 , competitiveness @cite_22 , initial attractiveness @cite_44 , or capacity constraints @cite_29 . Jost and Joy @cite_38 proposed an evolving model for social networks, where each person prefers to be friend with the friends of its friends. Friendship between two persons also depends on their mutual affinity, intimacy, attachment and understanding between them. WX @cite_15 proposed a model based on the mutual attraction. @cite_41 @cite_2 have proposed local world models based on the concept of local world connectivity. @cite_37 @cite_17 studied geographical constraint model, where a network is embedded in a two-dimensional geographic plain. @cite_32 @cite_34 proposed a self growing model, where existing nodes also make new connections in the future.
@cite_38 @cite_37 @cite_22 @cite_41 @cite_29 @cite_32 @cite_0 @cite_43 @cite_44 @cite_2 @cite_15 @cite_34 @cite_17
1964795149 2116173498 2043260340 2080434622 2063570818 2003893010 2104977387 2077698448 1953975752 2096334090
We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected ("make friends with the friends of your present friends"). We present simulation results for network parameters like the first eigenvalue of the graph Laplacian (synchronizability), clustering coefficients, average distances, and degree distributions for different distance preferences and compare them with the parameter values for random and scale-free networks. We find that for the shortest distance rule we obtain a power-law degree distribution as in scale-free networks, while the other parameters are significantly different, especially the clustering coefficient. We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from non-geographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied. The paper proposes a model which helps to investigate the competitive aspect of real networks in quantitative terms. Through theoretical analysis and numerical simulations, it shows that the competitive model has the universality for a weighted network. The relation between parameters in the weighted network and the competitiveness in the competitive network is obtained by theoretical analysis. Based on the expression of the degree distribution of the competitive network, the strength and degree distributions of the weighted network can be calculated. The analytical solution reveals that the degree distribution of the weighted network is correlated with the increment and initial value of edge weights, which is verified by numerical simulations. Moreover, the evolving pattern of a clustering coefficient along with network parameters such as the size of a network, an updating coefficient, an initial weight and the competitiveness are obtained by further simulations. We propose and study a novel evolving network model with the new concept of local-world connectivity, which exists in many physical complex networks. The local-world evolving network model represents a transition between power-law and exponential scaling, while the Barabasi–Albert scale-free model is only one of its special (limiting) cases. We found that this local-world evolving network model can maintain the robustness of scale-free networks and can improve the network reliance against intentional attacks, which is the inherent fragility of most scale-free networks. 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. 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. The rate at which nodes in a network increase their connectivity depends on their fitness to compete for links. For example, in social networks some individuals acquire more social links than others, or on the www some webpages attract considerably more links than others. We find that this competition for links translates into multiscaling, i.e. a fitness- dependent dynamic exponent, allowing fitter nodes to overcome the more connected but less fit ones. Uncovering this fitter-gets-richer phenomenon can help us understand in quantitative terms the evolution of many competitive systems in nature and society. In this paper, we introduce the concept of intrinsic strength which is used to describe the node's intrinsic property. Furthermore, we present a single preferential attachment model for the evolution of weighted networks in which the network growth is coupled with dynamical evolution of weights and intrinsic strength. The model yields a nontrivial time evolution of nodes' properties and generalized power law distributions for the weight, strength and degree, as confirmed in many real networks. The numerical simulation results are in good agreement with the analytical expressions. The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites. We find the exact form of the stationary distribution of the number of incoming links of sites in the limit of long times, Pq, and the long-time limit of the average connectivity qs, t of a site s at time t (one site is added per unit of time). At long times, Pq q 2g at q ! For most complex networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a mutual attraction model to characterize weighted evolving networks. By introducing the initial attractiveness A and the general mechanism of mutual attraction (controlled by parameter m), our model can naturally reproduce scale-free distributions of degree, weight, and strength, as found in many real systems. Also, simulation results are consistent with theoretical predictions. Interestingly, we obtain nontrivial clustering coefficient C and tunable degree assortativity r, depending on the values of m and A. Our model appears as a more general one that unifies the characterization of both assortative and disassortative weighted networks.