相关论文: Superdiffusion in a class of networks with margina…
In this paper, we propose a network whose nodes are labeled by the composite numbers and two nodes are connected by an undirected link if they are relatively prime to each other. As the size of the network increases, the network will be…
Complex network theory has shown success in understanding the emergent and collective behavior of complex systems [1]. Many real-world complex systems were recently discovered to be more accurately modeled as multiplex networks [2-6]---in…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1-r, or to the parent of the target node with probability…
We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
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…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Networks created and maintained by social processes, such as the human friendship network and the World Wide Web, appear to exhibit the property of navigability: namely, not only do short paths exist between any pair of nodes, but such…
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…