Related papers: Counting simplicial pairs in hypergraphs
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
We consider a multi-parameter model for randomly constructing simplicial complexes. This model interpolates between random clique complexes and Linial-Meshulam random $k$-dimensional complexes, two models that have been extensively studied.…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
Real-world graphs are massive in size and we need a huge amount of space to store them. Graph compression allows us to compress a graph so that we need a lesser number of bits per link to store it. Of many techniques to compress a graph, a…
Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry. This is why the focus of the…
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…
Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we…
We introduce the notion of k-hyperclique complexes, i.e., the largest simplicial complexes on the set [n] with a fixed k-skeleton. These simplicial complexes are a higher-dimensional analogue of clique (or flag) complexes (case k=2) and…
In Chung-Lu random graphs, a classic model for real-world networks, each vertex is equipped with a weight drawn from a power-law distribution, and two vertices form an edge independently with probability proportional to the product of their…
We use an n-spin system with permutation symmetric zz-interaction for simulating arbitrary pair-interaction Hamiltonians. The calculation of the required time overhead is mathematically equivalent to a separability problem of n-qubit…
Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…
The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and…
We show that the discrete versions of the systolic inequality that estimate the number of vertices of a simplicial complex from below have substantial applications to graphs, the one-dimensional simplicial complexes. Almost directly they…
Hypergraphs extend traditional networks by capturing multi-way or group interactions. Given the complexity of hypergraph data and the wide range of methodology available for pairwise network analysis, hypergraph data is often projected onto…
Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…
Given an arbitrary hypergraph $\mathcal{H}$, we may glue to $\mathcal{H}$ a family of hypergraphs to get a new hypergraph $\mathcal{H}'$ having $\mathcal{H}$ as an induced subhypergraph. In this paper, we introduce three gluing techniques…
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…
A hypergraph generalizes the concept of an ordinary graph. In an ordinary graph, edges connect pairs of vertices, whereas in a hypergraph, hyperedges can connect multiple vertices at a time. In this paper, we obtain a relationship between…