相关论文: Node-node distance distribution for growing networ…

We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…

This letter presents a unified analytical framework for internodal distance distributions in 2D and 3D wireless networks, with nodes confined to concentric circular or spherical regions. Four deployment scenarios are considered, covering…

A social network grows over a period of time with the formation of new connections and relations. In recent years we have witnessed a massive growth of online social networks like Facebook, Twitter etc. So it has become a problem of extreme…

A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…

When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…

Evolutionary mechanism in a self-organized system cause some functional changes that force to adapt new conformation of the interaction pattern between the components of that system. Measuring the structural differences one can retrace the…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission…

Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries).…

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…

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…

A widely studied model for generating sequences is to ``evolve'' them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally ``far apart'' in terms of variational distance.

Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including small world and scale free networks). They model a variety of phenomena, including the…

We investigate the time evolution of disease spread on a network by using the concept of generations. We derive a set of equations, which can be used to determine the average epidemic size. We find a very good agreement between the…

A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…

We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…

Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of…

The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain\'s dynamic properties at the ground level. Karbowski derived a power-law decay…

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…

Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the…