Related papers: Randomizing hypergraphs preserving degree correlat…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, i.e., those between two individuals.…
Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…
Real-world networks evolve over time via additions or removals of vertices and edges. In current network evolution models, vertex degree varies or grows arbitrarily. A recently introduced degree-preserving network growth (DPG) family of…
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
A directed hypergraph, which consists of nodes and hyperarcs, is a higher-order data structure that naturally models directional group interactions (e.g., chemical reactions of molecules). Although there have been extensive studies on local…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
Node classification on static graphs has achieved significant success, but achieving accurate node classification on dynamic graphs where node topology, attributes, and labels change over time has not been well addressed. Existing methods…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
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…