Related papers: Global and local observability of hypergraphs
This paper develops a method to conduct causal inference in the presence of unobserved confounders by leveraging networks with homophily, a frequently observed tendency to form edges with similar nodes. I introduce a concept of asymptotic…
Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…
Let $v$ be a vertex of a graph $G$. By the local complementation of $G$ at $v$ we mean to complement the subgraph induced by the neighbors of $v$. This operator can be generalized as follows. Assume that, each edge of $G$ has a label in the…
In this paper we propose a new observability property for nonautonomous linear control systems in finite dimension: the nonuniform complete observability, which is more general than the uniform complete observability. A dual relationship is…
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable…
Hypergraphs, which belong to the family of higher-order networks, are a natural and powerful choice for modeling group interactions in the real world. For example, when modeling collaboration networks, which may involve not just two but…
Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes…
Eigenvector centrality is a standard network analysis tool for determining the importance of (or ranking of) entities in a connected system that is represented by a graph. However, many complex systems and datasets have natural multi-way…
Real-world graphs are typically complex, exhibiting heterogeneity in the global structure, as well as strong heterophily within local neighborhoods. While a growing body of literature has revealed the limitations of common graph neural…
Spectral hypergraph theory mainly concerns using hypergraph spectra to obtain structural information about the given hypergraphs. The study of cospectral hypergraphs is important since it reveals which hypergraph properties cannot be…
A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to…
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…
Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have…
A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}$. The system's state $x$ is…
In [1], it is established that a convergent observer with an infinite gain margin can be designed for a given nonlinear system when a Riemannian metric showing that the system is differentially detectable (i.e., the Lie derivative of the…
This paper studies linear time-invariant descriptor systems which are not necessarily regular. We introduce the notion of partial detectability and characterize this concept by means of a simple rank criterion involving the system…
Graph representation learning based on graph neural networks (GNNs) can greatly improve the performance of downstream tasks, such as node and graph classification. However, the general GNN models do not aggregate node information in a…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…
Conditions are presented for different types of identifiability of discrete variable models generated over an undirected graph in which one node represents a binary hidden variable. These models can be seen as extensions of the latent class…