Related papers: Counting unlabelled multigraphs with three nodes
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Many real-world networks have associated metadata that assigns categorical labels to nodes. Analysis of these annotations can complement the topological analysis of complex networks. Annotated networks have typically been used to evaluate…
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…
Networks model the architecture backbone of complex systems. The backbone itself can change over time leading to what is called `temporal networks'. Interpreting temporal networks as trajectories in graph space of a latent graph dynamics…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
Models of growing networks are a central topic in network science. In these models, vertices are usually labeled by their arrival time, distinguishing even those node pairs whose structural roles are identical. In contrast, unlabeled…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent…
Heterogeneous graph neural networks aim to discover discriminative node embeddings and relations from multi-relational networks.One challenge of heterogeneous graph learning is the design of learnable meta-paths, which significantly…
This study poses the feature correspondence problem as a hypergraph node labeling problem. Candidate feature matches and their subsets (usually of size larger than two) are considered to be the nodes and hyperedges of a hypergraph. A…
Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…
In this paper, we introduce a class of graphs which we call average hereditary graphs. Many graphs that occur in the usual graph theory applications belong to this class of graphs. Many popular types of graphs fall under this class, such as…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node…
In network theory, a triad census is a method designed to categorize and enumerate the various types of subgraphs with three nodes and their connecting edges within a network. Triads serve as fundamental building blocks for comprehending…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…
We present a simple encoding for unlabeled noncrossing graphs and show how its latent counterpart helps us to represent several families of directed and undirected graphs used in syntactic and semantic parsing of natural language as…