Related papers: Complete Graphs and Polyominoes

Motivated by a recent extension of the zero-one law by Kolaitis and Kopparty, we study the distribution of the number of copies of a fixed disconnected graph in the random graph $G(n,p)$. We use an idea of graph decompositions to give a…

We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of…

The modular decomposition of a graph is a canonical representation of its modules. Algorithms for computing the modular decomposition of directed and undirected graphs differ significantly, with the undirected case being simpler, and…

We investigate random partitions of complete graphs defined by Poissonian emsembles of Markov loops

We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They…

Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…

Co-occurence networks can be adequately modeled by hyper-bag-graphs (hb-graphs for short). A hb-graph is a family of multisets having same universe, called the vertex set. An efficient exchange-based diffusion scheme has been previously…

Recent studies reveal the connection between GNNs and the diffusion process, which motivates many diffusion-based GNNs to be proposed. However, since these two mechanisms are closely related, one fundamental question naturally arises: Is…

We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph…

Our aim is to study the Total Variation Flow in Metric Graphs. First, we define the functions of bounded variation in Metric Graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness…

A new complete invariant for acyclic graphs is presented

We study the problem of fair division of a set of indivisible goods with connectivity constraints. Specifically, we assume that the goods are represented as vertices of a connected graph, and sets of goods allocated to the agents are…

Graph learning plays a pivotal role and has gained significant attention in various application scenarios, from social network analysis to recommendation systems, for its effectiveness in modeling complex data relations represented by graph…

We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…

We study analytically the plasmonic modes in the graphene-coated dielectric nanowire, based on the explicit form of nonlinear surface conductivity of graphene. The propagation constants of different plasmonic modes can be tuned by the input…

Graph diffusion models have recently been proposed to synthesize entire graphs, such as molecule graphs. Although existing methods have shown great performance in generating entire graphs for graph-level learning tasks, no graph diffusion…

We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and…

The specifics of charge screening and electrostatic potential spatial distribution in multilayered graphene films placed in between charged substrates is theoretically analyzed. It is shown that by varying the areal charge densities on the…