Related papers: The evolution of navigable small-world networks
This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual…
We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the…
Graphs are called navigable if one can find short paths through them using only local knowledge. It has been shown that for a graph to be navigable, its construction needs to meet strict criteria. Since such graphs nevertheless seem to…
Small-world networks (SWN) are found to be closer to the real social systems than both regular and random lattices. Then, a model for the evolution of economic systems is generalized to SWN. The Sznajd model for the two-state opinion…
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
We study navigation with limited information in networks and demonstrate that many real-world networks have a structure which can be described as favoring communication at short distance at the cost of constraining communication at long…
We study the dynamics of an epidemic-like model for the spread of a rumor on a small-world network. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network…
Background: Imagine a paper with n nodes on it where each pair undergoes a coin toss experiment; if heads we connect the pair with an undirected link, while tails maintain the disconnection. This procedure yields a random graph. Now…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabasi-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing…
Representation learning over graph structure data has been widely studied due to its wide application prospects. However, previous methods mainly focus on static graphs while many real-world graphs evolve over time. Modeling such evolution…
The mathematical study of the small-world concept has fostered quite some interest, showing that small-world features can be identified for some abstract classes of networks. However, passing to real complex systems, as for instance…
Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the…
The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation…
The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…
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 the distribution of their inter--point network distances. Our…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…