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The importance of higher-order relations is widely recognized in a large number of real-world systems. However, annotating them is a tedious and sometimes impossible task. Consequently, current approaches for data modelling either ignore…
We study core-periphery structure in networks using inference methods based on a flexible network model that allows for traditional onion-like cores within cores, but also for hierarchical tree-like structures and more general non-nested…
The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
Hypergraphs provide an effective modeling approach for modeling high-order relationships in many real-world datasets. To capture such complex relationships, several hypergraph neural networks have been proposed for learning hypergraph…
Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the…
The analysis of small recurrent substructures, so called network motifs, has become a standard tool of complex network science to unveil the design principles underlying the structure of empirical networks. In many natural systems network…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…
The conventional definition of hypergraph has two major issues: (1) there is not a standard definition of directed hypergraph and (2) there is not a formal definition of nested hypergraph. To resolve these issues, we propose a new…
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…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
Asymmetric relational data is increasingly prevalent across diverse fields, underscoring the need for directed network models to address the complex challenges posed by their unique structures. Unlike undirected models, directed models can…
High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases…
We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…
This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the…
Networks provide an informative, yet non-redundant description of complex systems only if links represent truly dyadic relationships that cannot be directly traced back to node-specific properties such as size, importance, or coordinates in…