We consider two different models of small-world graphs on nodes whose locations are
modelled by a stochastic point process. In the first model each node is connected to a fixed …

In a recent paper, Kleinberg (2000) considered a small-world network model consisting of a
d-dimensional lattice augmented with shortcuts. The probability of a shortcut being present …

In Chung-Lu random graphs, a classic model for real-world networks, each vertex is
equipped with a weight drawn from a power-law distribution, and two vertices form an edge …

Small world models are networks consisting of many local links and fewer long
rangeshortcuts', used to model networks with a high degree of local clustering but relatively …

Small world models are networks consisting of many local links and fewer long range
'shortcuts'. In this paper, we consider some particular instances, and rigorously investigate …

In this paper we study decentralized routing in small-world networks that combine a wide
variation in node degrees with a notion of spatial embedding. Specifically, we consider a …

We analyze the properties of Small-World networks, where links are much more likely to
connect" neighbor nodes" than distant nodes. In particular, our analysis provides new results …

The small world phenomenon, that consistently occurs in numerous existing networks, refers
to two similar but different properties—small average distance and the clustering effect. We …

Substantial research has been devoted to the modelling of the small-world phenomenon
that arises in nature as well as human society. Earlier work has focused on the static …

We present an exact description of a crossover between two different regimes of simple
analogies of small-world networks. Each of the sites chosen with a probability $ p $ from $ n …