Related papers: Complete Graphs and Polyominoes
Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…
We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2-colorings of intervals, as statistical Ramsey theory…
We study a variant of the dispersion process on the complete graph introduced in the recent work [17] under the mean-field framework. We adopt a kinetic perspective (as opposed to the probabilistic approach taken in [17] and many other…
The full counting statistics of the charge transport through an undoped graphene sheet in the presence of smooth disorder is studied. At the Dirac point both in clean and diffusive limits, transport properties of a graphene sample are…
The phase diagram of soft spheres with size dispersion has been studied by means of an optimized Monte Carlo algorithm which allows to equilibrate below the kinetic glass transition for all sizes distribution. The system ubiquitously…
The propagation of a surface plasmon-polariton along a stack of doped graphene sheets is considered. This auxiliary problem is used to discuss: (i) the scattering of such a mode at an interface between the stack and the vacuum; (ii) the…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
This short note is a supplement to [1], in which the total variation of graph distributional signals is introduced and studied. We introduce a different formulation of total variation and relate it to the notion of edge centrality. The…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
We enumerate factorisations of the complete bipartite graph into spanning semiregular graphs in several cases, including when the degrees of all the factors except one or two are small. The resulting asymptotic behaviour is seen to…
We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…
Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…
We introduce, test and discuss a method for classifying and clustering data modeled as directed graphs. The idea is to start diffusion processes from any subset of a data collection, generating corresponding distributions for reaching…
Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are…
We show that if a graph contains few induced copies of a given graph then its edges are distribited unevenly.
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
Recent years have seen a rise in the development of representational learning methods for graph data. Most of these methods, however, focus on node-level representation learning at various scales (e.g., microscopic, mesoscopic, and…
Graph generation addresses the problem of generating new graphs that have a data distribution similar to real-world graphs. While previous diffusion-based graph generation methods have shown promising results, they often struggle to scale…
We review the problem of finding paths in Cayley graphs of groups and group actions, using the Rubik's cube as an example, and we list several more examples of significant mathematical interest. We then show how to formulate these problems…