Related papers: Geometric Graph Properties of the Spatial Preferre…
Preferential attachment is an appealing mechanism for modeling power-law behavior of the degree distributions in directed social networks. In this paper, we consider methods for fitting a 5-parameter linear preferential model to network…
We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism…
The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to a…
We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to…
Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
Metric graphs are useful tools for describing spatial domains like road and river networks, where spatial dependence act along the network. We take advantage of recent developments for such Gaussian Random Fields (GRFs), and consider joint…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
A remarkable approach for grasping the relevant statistical features of real networks with the help of random graphs is offered by hyperbolic models, centred around the idea of placing nodes in a low-dimensional hyperbolic space, and…
In the classical preferential attachment model, links form instantly to newly arriving nodes and do not change over time. We propose a hierarchical random graph model in a spatial setting, where such a time-variability arises from an…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…