Related papers: Betweenness Centrality in Dense Random Geometric N…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
Betweenness centrality---measuring how many shortest paths pass through a vertex---is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [J. Math.…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
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…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
A geometric graph is a graph embedded in the plane with vertices at points and edges drawn as curves (which are usually straight line segments) between those points. The average transversal complexity of a geometric graph is the number of…
Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the…
Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link…
The directed landscape is a random directed metric on the plane that arises as the scaling limit of metric models in the KPZ universality class. For a pair of points p, q, the disjointness gap G(p; q) measures the shortfall when we optimize…
A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…
In this work, we use the theory of spatial networks to analyze galaxy distributions. The aim is to develop new approaches to study the spatial galaxy environment properties by means of the network parameters. We investigate how each of the…
We consider a crucial aspect of self-organization of a sensor network consisting of a large set of simple sensor nodes with no location hardware and only very limited communication range. After having been distributed randomly in a given…
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
A neural network targeting at unsupervised image anomaly localization, called the PEDENet, is proposed in this work. PEDENet contains a patch embedding (PE) network, a density estimation (DE) network, and an auxiliary network called the…
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…
Shortest paths are representative of discrete geodesic distances in graphs, and many descriptors of networks depend on their counting. In multiplex networks, this counting is radically important to quantify the switch between layers and it…