Related papers: Growing Graphs with Hyperedge Replacement Graph Gr…
In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…
Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We…
Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general…
Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…
Counterfactual examples have emerged as an effective approach to produce simple and understandable post-hoc explanations. In the context of graph classification, previous work has focused on generating counterfactual explanations by…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…
Traditional classification tasks learn to assign samples to given classes based solely on sample features. This paradigm is evolving to include other sources of information, such as known relations between samples. Here we show that, even…
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…
Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational…
If $\Gamma$ is a graph for which every edge is in exactly one clique of order $\omega$, then one can form a new graph with vertex set equal to these cliques. This is a generalization of the line graph of $\Gamma$. We discover many general…
Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory,…
A rough structure theorem is proved for graphs $G$ containing no copy of a bounded degree tree $T$: from any such $G$, one can delete $o(|G||T|)$ edges in order to get a subgraph all of whose connected components have a cover of order…
Hyperbolic random graphs inherit many properties that are present in real-world networks. The hyperbolic geometry imposes a scale-free network with a strong clustering coefficient. Other properties like a giant component, the small world…
Treewidth is a parameter that emerged from the study of minor closed classes of graphs (i.e. classes closed under vertex and edge deletion, and edge contraction). It in some sense describes the global structure of a graph. Roughly, a graph…
Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in…