Related papers: Spectral Detection of Simplicial Communities via H…

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…

Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial…

This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…

Numerous networked systems feature a structure of nontrivial communities, which often correspond to their functional modules. Such communities have been detected in real-world biological, social and technological systems, as well as in…

As a generalization of the use of graphs to describe pairwise interactions, simplicial complexes can be used to model higher-order interactions between three or more objects in complex systems. There has been a recent surge in activity for…

Community detection has been one of the central problems in network studies and directed network is particularly challenging due to asymmetry among its links. In this paper, we found that incorporating the direction of links reveals new…

We introduce a method for the detection of Statistically Validated Simplices in higher-order networks. Statistically validated simplices represent the maximal sets of nodes of any size that consistently interact collectively and do not…

Higher-order networks are gaining significant scientific attention due to their ability to encode the many-body interactions present in complex systems. However, higher-order networks have the limitation that they only capture many-body…

Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to the…

Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that…

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…

Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem…

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

This article considers spectral community detection in the regime of sparse networks with heterogeneous degree distributions, for which we devise an algorithm to efficiently retrieve communities. Specifically, we demonstrate that a…

Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…

Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…

Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper…

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…

Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly…

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this…