Related papers: Recursive Formula for Labeled Graph Enumeration
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in the…
The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…
Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…
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…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
The Caporaso-Harris formula gives a recursive algorithm to enumerate delta nodal degree d curves in P^2. The recursion is obtained in terms of curves of lower degree that are tangent to a given divisor. This paper presents two…
Many social networks exhibit assortative mixing so that the predictions of uncorrelated models might be inadequate. To analyze the role of assortativity we introduce an algorithm which changes correlations in a network and produces…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…