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We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…
For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
This manuscript introduces Diophantine labeling, a new way of labeling of the vertices for finite simple undirected graphs with some divisibility condition on the edges. Maximal graphs admitting Diophantine labeling are investigated and…
This work considers the problem of heterogeneous graph-level anomaly detection. Heterogeneous graphs are commonly used to represent behaviours between different types of entities in complex industrial systems for capturing as much…
We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also give a complete description of the…
We compute numerically the homology of several graph complexes in low loop orders, extending previous results.
Topological phases of noninteracting particles are distinguished by global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses…
We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
Heterogeneous graph neural networks (HGNs) are prominent approaches to node classification tasks on heterogeneous graphs. Despite the superior performance, insights about the predictions made from HGNs are obscure to humans. Existing…
We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological…
Exponential-family random graph models (ERGMs) are probabilistic network models that are parametrized by sufficient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing system…
Machine learning models that learn from dynamic graphs face nontrivial challenges in learning and inference as both nodes and edges change over time. The existing large-scale graph benchmark datasets that are widely used by the community…