Abstract:
Many realistic networks have community structures, namely, a network consists of groups of nodes within which links are dense but among which links are sparse. This paper proposes a growing network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Also, it utilizes the preferential attachment for building connections determined by nodes' strengths, which evolves dynamically during the growth of the system. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes' degrees and strengths.

Abstract:
We investigate the effect of risk estimate on the spread of diseases by the standard susceptible--infected--susceptible (SIS) model. The perception of therisk of being infected is explained as cutting off links among individuals, either healthy or infected. We study this simple dynamics on scale-free networks by analytical methods and computer simulations. We obtain the self-consistency form for the infection prevalence in steady states. For a given transmission rate, there exists a linear relationship between the reciprocal of the density ofinfected nodes and the estimate parameter. We confirm all the results by sufficient numerical simulations.

Abstract:
The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Employing growth and preferential attachment mechanisms, we generate networks with a generalized power-law distribution of nodes' degrees.

Abstract:
A rank-dependent deactivation mechanism is introduced to network evolution. The growth dynamics of the network is based on a finite memory of individuals, which is implemented by deactivating one site at each time step. The model shows striking features of a wide range of real-world networks: power-law degree distribution, high clustering coefficient, and disassortative degree correlation.

Abstract:
We investigate the standard susceptible-infected-susceptible model on a random network to study the effects of preference and geography on diseases spreading. The network grows by introducing one random node with $m$ links on a Euclidean space at unit time. The probability of a new node $i$ linking to a node $j$ with degree $k_j$ at distance $d_{ij}$ from node $i$ is proportional to $k_{j}^{A}/d_{ij}^{B}$, where $A$ and $B$ are positive constants governing preferential attachment and the cost of the node-node distance. In the case of A=0, we recover the usual epidemic behavior with a critical threshold below which diseases eventually die out. Whereas for B=0, the critical behavior is absent only in the condition A=1. While both ingredients are proposed simultaneously, the network becomes robust to infection for larger $A$ and smaller $B$.

Abstract:
We study geographical effects on the spread of diseases in lattice-embedded scale-free networks. The geographical structure is represented by the connecting probability of two nodes that is related to the Euclidean distance between them in the lattice. By studying the standard Susceptible-Infected model, we found that the geographical structure has great influences on the temporal behavior of epidemic outbreaks and the propagation in the underlying network: the more geographically constrained the network is, the more smoothly the epidemic spreads.

Abstract:
Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive aging mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, $C(k) \sim k^{-1}$ and $C \sim n^{-1}$, where $k$ and $n$ refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and aging of networks where intrinsic features of individual nodes drive their popularity, and hence degree.

Abstract:
Many real networks are embedded in a metric space: the interactions among individuals depend on their spatial distances and usually take place among their nearest neighbors. In this paper, we introduce a modified susceptible-infected-susceptible (SIS) model to study geographical effects on the spread of diseases by assuming that the probability of a healthy individual infected by an infectious one is inversely proportional to the Euclidean distance between them. It is found that geography plays a more important role than hubs in disease spreading: the more geographically constrained the network is, the more highly the epidemic prevails.

Abstract:
This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is determined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.