Related papers: Stochastic graph Voronoi tessellation reveals comm…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
The pair correlation function (PCF) has proven an effective tool for analyzing many physical systems due to its simplicity and its applicability to simulated and experimental data. However, as an averaged quantity, the PCF can fail to…
For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…
Many online networks are measured and studied via sampling techniques, which typically collect a relatively small fraction of nodes and their associated edges. Past work in this area has primarily focused on obtaining a representative…
This paper considers the problem of community detection on multiple potentially correlated graphs from an information-theoretical perspective. We first put forth a random graph model, called the multi-view stochastic block model (MVSBM),…
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set…
Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game…
We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity…
Temporal network analysis and time evolution of network characteristics are powerful tools in describing the changing topology of dynamic networks. This paper uses such approaches to better visualize and provide analytical measures for the…
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…
We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing to encode such structures into labeled maps with a…
A number of recent studies have focused on the statistical properties of networked systems such as social networks and the World-Wide Web. Researchers have concentrated particularly on a few properties which seem to be common to many…
3D Voronoi's tessellation method was first applied to identify groups of galaxies in the structure of a supercluster. The sample under consideration consists of more than 7000 galaxies of the Local Supercluster (LS) with radial velocities…
When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…
Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…