Related papers: Heterogeneous network with distance dependent conn…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
Networks of disparate phenomena-- be it the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions-- exhibit broadly consistent architectural features. To explain this, we propose a new…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…
We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time $t$ are distributed homogeneously between a new node and the exising nodes selected uniformly. This is…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…