相关论文: Random Networks Growing Under a Diameter Constrain…

Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…

Many real-world networks have properties of small-world networks, with clustered local neighborhoods and low average-shortest path (ASP). They may also show a scale-free degree distribution, which can be generated by growth and preferential…

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular those mediated by the Internet). We use analytical and…

Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…

Here, we propose a class of scale-free networks $G(t;m)$ with some intriguing properties, which can not be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including (i)…

We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found…

In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…

We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in…

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…

We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…

Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…

This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…

We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…

We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of…

A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…

Random scale-free overlay topologies provide a number of properties like for example high resilience against failures of random nodes, small (average) diameter as well as good expansion and congestion characteristics that make them…