Related papers: Smallworldness in Hypergraphs
We propose a generalization of small world networks, in which the reconnection of links is governed by a function that depends on the distance between the elements to be linked. An adequate choice of this function lets us control the…
A regular lattice in which the sites can have long range connections at a distance l with a probabilty $P(l) \sim l^{-\delta}$, in addition to the short range nearest neighbour connections, shows small-world behaviour for $0 \le \delta <…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…
We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local…
Many natural, technological, and social systems incorporate multiway interactions, yet are characterized and measured on the basis of weighted pairwise interactions. In this article, I propose a family of models in which pairwise…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…
Networks that are organized as a hierarchy of modules have been the subject of much research, mainly focusing on algorithms that can extract this community structure from data. The question of why modular hierarchical organizations are so…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
In recent years, there has been growing interest in the study of coevolutionary games on networks. Despite much progress, little attention has been paid to spatially embedded networks, where the underlying geographic distance, rather than…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
Small-world networks are networks in which the graphical diameter of the network is as small as the diameter of random graphs but whose nodes are highly clustered when compared with the ones in a random graph. Examples of small-world…
The small-world phenomenon in complex networks has been identified as being due to the presence of long-range links, i.e., links connecting nodes that would otherwise be separated by a long node-to-node distance. We find, surprisingly, that…
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…
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…
Recent studies have shown that novel collective behaviors emerge in complex systems due to the presence of higher-order interactions. However, how the collective behavior of a system is influenced by the microscopic organization of its…
We construct a model of wealth distribution, based on an interactive multiplicative stochastic process on static complex networks. Through numerical simulations we show that a decrease in the number of links discourages equality in wealth…
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…
In recent years, new algorithms and cryptographic protocols based on the laws of quantum physics have been designed to outperform classical communication and computation. We show that the quantum world also opens up new perspectives in the…