Concept
Graph operations
Related publications (133)
BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS
Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...
Siam Publications2024Non-planarity of Markoff graphs mod p
We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...
Berlin2024A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane
Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
Electronic Journal Of Combinatorics2024The Power of Two Matrices in Spectral Algorithms for Community Recovery
Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...
Ieee-Inst Electrical Electronics Engineers Inc2024Brain Fingerprinting Using Fmri Spectral Signatures On High-Resolution Cortical Graphs
Dimitri Nestor Alice Van De Ville, Maria Giulia Preti, Hamid Behjat, Stefano Moia, Carlo Ferritto
Resting-state fMRI has proven to entail subject-specific signatures that can serve as a fingerprint to identify individuals. Conventional methods are based on building a connectivity matrix based on correlation between the average time course of pairs of b ...
IEEE2023Maximum Independent Set: Self-Training through Dynamic Programming
Volkan Cevher, Grigorios Chrysos, Efstratios Panteleimon Skoulakis
This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly construc ...
2023A full characterization of invariant embeddability of unimodular planar graphs
When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...
WILEY2023Frequent asymmetric migrations suppress natural selection in spatially structured populations
Anne-Florence Raphaëlle Bitbol, Alia Abbara
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently symmetric structures, ev ...
Oxford2023Nature vs. Nurture: Feature vs. Structure for Graph Neural Networks
Karl Aberer, Thành Tâm Nguyên, Chi Thang Duong
Graph neural networks take node features and graph structure as input to build representations for nodes and graphs. While there are a lot of focus on GNN models, understanding the impact of node features and graph structure to GNN performance has received ...
ELSEVIER2022On the robustness of the metric dimension of grid graphs to adding a single edge
Patrick Thiran, Gergely Odor, Satvik Mehul Mashkaria
The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to t ...
2022