A deterministic small-world network created by edge iterations

Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections. Here we present a model that generates a small-world network in a simple deterministic way. Our model has a discrete exponential degree distribution. We solve the main characteristics of the model.Comment: 9 pages, 1 figure. to appear in Physica

Self-Organization of Wireless Ad Hoc Networks as Small Worlds Using Long Range Directional Beams

We study how long range directional beams can be used for self-organization of a wireless network to exhibit small world properties. Using simulation results for randomized beamforming as a guideline, we identify crucial design issues for algorithm design. Subsequently, we propose an algorithm for deterministic creation of small worlds. We define a new centrality measure that estimates the structural importance of nodes based on traffic flow in the network, which is used to identify the optimum nodes for beamforming. This results in significant reduction in path length while maintaining connectivity.Comment: Accepted to Joint workshop on complex networks and pervasive group communication (CCNet/PerGroup), in conjunction with IEEE Globecom 201

Deterministic Small-World Networks

Many real life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two nodes). These networks have been characterized as small-world networks and modeled by the addition of randomness to regular structures. We show that small-world networks can be constructed in a deterministic way. This exact approach permits a direct calculation of relevant network parameters allowing their immediate contrast with real-world networks and avoiding complex computer simulations.Comment: 6 pages, 1 figur

Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels.Comment: 16 pages, 2 figure

A Quality and Cost Approach for Comparison of Small-World Networks

We propose an approach based on analysis of cost-quality tradeoffs for comparison of efficiency of various algorithms for small-world network construction. A number of both known in the literature and original algorithms for complex small-world networks construction are shortly reviewed and compared. The networks constructed on the basis of these algorithms have basic structure of 1D regular lattice with additional shortcuts providing the small-world properties. It is shown that networks proposed in this work have the best cost-quality ratio in the considered class.Comment: 27 pages, 16 figures, 1 tabl

On the performance of routing algorithms in wormhole-switched multicomputer networks

This paper presents a comparative performance study of adaptive and deterministic routing algorithms in wormhole-switched hypercubes and investigates the performance vicissitudes of these routing schemes under a variety of network operating conditions. Despite the previously reported results, our results show that the adaptive routing does not consistently outperform the deterministic routing even for high dimensional networks. In fact, it appears that the superiority of adaptive routing is highly dependent to the broadcast traffic rate generated at each node and it begins to deteriorate by growing the broadcast rate of generated message