Related papers: Connected components in networks with higher-order…
Rapid discovery of new reactions and molecules in recent years has been facilitated by the advancements in high throughput screening, accessibility to a much more complex chemical design space, and the development of accurate molecular…
Evaluating node importance is a critical aspect of analyzing complex systems, with broad applications in digital marketing, rumor suppression, and disease control. However, existing methods typically rely on conventional network structures…
A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical…
Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…
Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
A temporal (directed) graph is a graph whose edges are available only at specific times during its lifetime, $\tau$. Paths are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasingly…
We introduce a new operad-like structure that we call a reconnectad; the ``input'' of an element of a reconnectad is a finite simple graph, rather than a finite set, and ``compositions'' of elements are performed according to the notion of…
Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as…
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…
Hypergraph offers a framework to depict the multilateral relationships in real-world complex data. Predicting higher-order relationships, i.e hyperedge, becomes a fundamental problem for the full understanding of complicated interactions.…
Hypergraphs model higher-order relations that drive real-world decisions, from drug prescriptions to recommendations. A central structural signal in such data, beyond what pairwise relations can express, is interaction compositionality:…
Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…
From social to biological systems, many real-world systems are characterized by higher-order, non-dyadic interactions. Such systems are conveniently described by hypergraphs, where hyperedges encode interactions among an arbitrary number of…
Hypergraphs have been a recent focus of study in mathematical data science as a tool to understand complex networks with high-order connections. One question of particular relevance is how to leverage information carried in hypergraph…
One of the key aspects in component-based design is specifying the software architecture that characterizes the topology and the permissible interactions of the components of a system. To achieve well-founded design there is need to address…
Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…
We define a $q$-linear path in a hypergraph $H$ as a sequence $(e_1,\ldots,e_L)$ of edges of $H$ such that $|e_i \cap e_{i+1}| \in [\![1,q]\!]$ and $e_i \cap e_j=\varnothing$ if $|i-j|>1$. In this paper, we study the connected components…
An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classification of signed graphs to oriented…
A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…