Related papers: Graphical Fermat's Principle and Triangle-Free Gra…
In this paper we show how to efficiently produce unbiased estimates of subgraph frequencies from a probability sample of egocentric networks (i.e., focal nodes, their neighbors, and the induced subgraphs of ties among their neighbors). A…
This paper has dual aims. First is to develop practical universal coding methods for unlabeled graphs. Second is to use these for graph anomaly detection. The paper develops two coding methods for unlabeled graphs: one based on the degree…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
In a seminal paper, Chen, Roughgarden and Valiant studied cost sharing protocols for network design with the objective to implement a low-cost Steiner forest as a Nash equilibrium of an induced cost-sharing game. One of the most intriguing…
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
Undirected graphical models encode in a graph $G$ the dependency structure of a random vector $Y$. In many applications, it is of interest to model $Y$ given another random vector $X$ as input. We refer to the problem of estimating the…
Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
A graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et al. [8] provided a characterization of equimatchable graphs with girth at least $5$. In this paper, we extend this result by providing a…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a…
Graphs are ubiquitous real-world data structures, and generative models that approximate distributions over graphs and derive new samples from them have significant importance. Among the known challenges in graph generation tasks,…
Given a set $\xi=\{H_1,H_2,...\}$ of connected non acyclic graphs, a $\xi$-free graph is one which does not contain any member of $% \xi$ as copy. Define the excess of a graph as the difference between its number of edges and its number of…
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In this…
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in…
Given a graph $G$ cellularly embedded on a surface $\Sigma$ of genus $g$, a cut graph is a subgraph of $G$ such that cutting $\Sigma$ along $G$ yields a topological disk. We provide a fixed parameter tractable approximation scheme for the…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…