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We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem that involves a fid ...
An abstract topological graph (briefly an AT-graph) is a pair A = (G, X) where G = (V, E) is a graph and X. E2 is a set of pairs of its edges. The AT-graph A is simply realizable if G can be drawn in the plane so that each pair of edges from X crosses exac ...
One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in n^{3-o(1)} time, and it is widely open whether it has an O(n^{3-ε}) time algorithm for ε > 0. To better understand APSP, one often strives to obtain subcubic t ...
Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021
Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...
We study in this thesis the asymptotic behavior of optimal paths on a random graph model, the configuration model, for which we assign continuous random positive weights on its edges.
We start by describing the asymptotic behavior of the diameter and the f ...
We propose the Recursive Non-autoregressive Graph-to-graph Transformer architecture (RNG-Tr) for the iterative refinement of arbitrary graphs through the recursive application of a non-autoregressive Graph-to-Graph Transformer and apply it to syntactic dep ...
Let G be a drawing of a graph with n vertices and e > 4n edges, in which no two adjacent edges cross and any pair of independent edges cross at most once. According to the celebrated Crossing Lemma of Ajtai, Chvatal, Newborn, Szemeredi and Leighton, the nu ...
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale centrality measure. A n ...
The articles in this special section focus on graph signal processing. Generically, the networks that sustain our societies can be understood as complex systems formed by multiple nodes, where global network behavior arises from local interactions between ...
