Related papers: Expected Message Delivery Time for Small-world Net…
Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…
We study the efficiency of the gradient mechanism of message transfer in a $2-d$ communication network of regular nodes and randomly distributed hubs. Each hub on the network is assigned some randomly chosen capacity and hubs with lower…
Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among…
We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These…
Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…
We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…
In this Letter we investigate networks that have been optimized to realize a trade-off between enhanced synchronization and cost of wire to connect the nodes in space. Analyzing the evolved arrangement of nodes in space and their…
Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing…
We describe a distributed randomized algorithm computing approximate distances and routes that approximate shortest paths. Let n denote the number of nodes in the graph, and let HD denote the hop diameter of the graph, i.e., the diameter of…
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…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
Many networks extent in space, may it be metric (e.g. geographic) or non-metric (ordinal). Spatial network growth, which depends on the distance between nodes, can generate a wide range of topologies from small-world to linear scale-free…
We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically…
In this research report, we examine the effects of small-world network organization on spike synchronization dynamics in networks of Izhikevich spiking units. We interpolate network organizations from regular ring lattices, through the…
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…
In modern data center networks, thousands of hosts contend for shared link capacity; the scale of these systems makes centralized scheduling impractical. This article models such scheduling as a bipartite matching problem under…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
Let G=(V,E) be an undirected loopless graph with possible parallel edges and s and t be two vertices of G. Assume that vertex s is labelled at the initial time step and that every labelled vertex copies its labelling to neighbouring…
In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…