Related papers: The evolution of navigable small-world networks

Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…

We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…

We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…

We propose a growing model which interpolates between one-dimensional regular lattice and small-world networks. The model undergoes an interesting phase transition from large to small world. We investigate the structural properties by both…

Many geophysical processes can be modelled by using interconnected networks. The small-world network model has recently attracted much attention in physics and applied sciences. In this paper, we try to use and modify the small-world theory…

We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…

We establish a relationship between the Small-World behavior found in complex networks and a family of Random Walks trajectories using, as a linking bridge, a maze iconography. Simple methods to generate mazes using Random Walks are…

Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

Since their introduction by Kipf and Welling in $2017$, a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within a single observed graph and its feature matrix. Despite the…

The changing topology of a network is driven by the need to maintain or optimize network function. As this function is often related to moving quantities such as traffic, information, etc. efficiently through the network the structure of…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…

Quantitative descriptions of network structure in big data can provide fundamental insights into the function of interconnected complex systems. Small-world structure, commonly diagnosed by high local clustering yet short average path…

Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…

Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…

Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…

In the classical Erd\"os-R\'enyi random graph G(n,p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n,p) is homogeneous in the sense that all vertices have the same…

Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…