Related papers: Observability of Hypergraphs
The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite,…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…
Graphs are one of the most efficacious structures for representing datapoints and their relations, and they have been largely exploited for different applications. Previously, the higher-order relations between the nodes have been modeled…
Hypergraphs, graph generalizations where edges are conglomerates of $r$ nodes called hyperedges of rank $r\geq 2$, are excellent models to study systems with interactions that are beyond the pairwise level. For hypergraphs, the node degree…
Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
Graph neural network (GNN) has gained increasing popularity in recent years owing to its capability and flexibility in modeling complex graph structure data. Among all graph learning methods, hypergraph learning is a technique for exploring…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Understanding human mobility is essential for applications ranging from urban planning to public health. Traditional mobility models such as flow networks and colocation matrices capture only pairwise interactions between discrete…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…
Graph representation learning based on graph neural networks (GNNs) can greatly improve the performance of downstream tasks, such as node and graph classification. However, the general GNN models do not aggregate node information in a…
We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
In network science, collective dynamics of complex systems are typically modelled as (nonlinear, often including many-body) vertex-level update rules evolving over a graph interaction structure. In recent years, frameworks that explicitly…