Related papers: Implementing a Metropolis sampler on decomposable …

Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…

We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem…

Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as…

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…

Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory,…

Forbidden characterizations may sometimes be the most natural way to describe families of graphs, and yet these characterizations are usually very hard to exploit for enumerative purposes. By building on the work of Gioan and Paul (2012)…

The Onion Decomposition has recently been shown to provide principled models of complex graphs that better reproduce the sparse networks found in nature, but at the cost of complicated connection rules. We propose a k-edge swapping MCMC…

Graph convolutional networks (GCNs) have achieved great success in graph representation learning by extracting high-level features from nodes and their topology. Since GCNs generally follow a message-passing mechanism, each node aggregates…

A \emph{locally irregular graph} is a graph whose adjacent vertices have distinct degrees. We say that a graph $G$ can be decomposed into $k$ locally irregular subgraphs if its edge set may be partitioned into $k$ subsets each of which…

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex…

How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…

Split decomposition of graphs was introduced by Cunningham (under the name join decomposition) as a generalization of the modular decomposition. This paper undertakes an investigation into the algorithmic properties of split decomposition.…

Many multivariate data such as social and biological data exhibit complex dependencies that are best characterized by graphs. Unlike sequential data, graphs are, in general, unordered structures. This means we can no longer use classic,…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

A decomposition of a graph is a set of subgraphs whose edges partition those of $G$. The 3-decomposition conjecture posed by Hoffmann-Ostenhof in 2011 states that every connected cubic graph can be decomposed into a spanning tree, a…

Integrating data from heterogeneous sources is often modeled as merging graphs. Given two or more 'compatible', but not-isomorphic graphs, the first step is to identify a graph alignment, where a potentially partial mapping of vertices…

Traditional classification tasks learn to assign samples to given classes based solely on sample features. This paradigm is evolving to include other sources of information, such as known relations between samples. Here we show that, even…

In this paper, we build on recent results by Chauve et al. (2014) and Bahrani and Lumbroso (2017), which combined the split-decomposition, as exposed by Gioan and Paul, with analytic combinatorics, to produce new enumerative results on…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…