相关论文: Eigenvector localization in hypergraphs: pair-wise…
Let $H=(V,E)$ be an $r$-uniform hypergraph with the vertex set $V$ and the edge set $E$. For $1\leq s \leq r/2$, we define a weighted graph $G^{(s)}$ on the vertex set ${V\choose s}$ as follows. Every pair of $s$-sets $I$ and $J$ is…
Higher-order interactions have recently emerged as a promising framework for describing new dynamical phenomena in heterogeneous contagion processes. However, a fundamental open question is how to understand their contribution from the…
A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous graphs typically employs meta-paths to deal with the heterogeneity by reducing the graph to a homogeneous network, guide random walks or capture…
Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the…
In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art…
Link Prediction on Hyper-relational Knowledge Graphs (HKG) is a worthwhile endeavor. HKG consists of hyper-relational facts (H-Facts), composed of a main triple and several auxiliary attribute-value qualifiers, which can effectively…
Cooperation plays a fundamental role in societal and biological domains, and the population structure profoundly shapes the dynamics of evolution. Practically, individuals behave either altruistically or egoistically in multiple groups,…
Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…
Real-world networks have high-order relationships among objects and they evolve over time. To capture such dynamics, many works have been studied in a range of fields. Via an in-depth preliminary analysis, we observe two important…
Temporal graph learning has applications in recommendation systems, traffic forecasting, and social network analysis. Although multiple architectures have been introduced, progress in positional encoding for temporal graphs remains limited.…
In this paper, we study the entries of the principal eigenvector of the signless Laplacian matrix of a hypergraph. More precisely, we obtain bounds for this entries. These bounds are computed trough other important parameters, such as…
Hypergraphs are data structures capable of capturing supra-dyadic relations. We can use them to model binary relations, but also to model groups of entities, as well as the intersections between these groups or the contained subgroups. In…
Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the…
Extending community detection from pairwise networks to hypergraphs introduces fundamental theoretical challenges. Hypergraphs exhibit structural heterogeneity with no direct graph analogue: hyperedges of varying orders can connect nodes…
Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
A two-dimensional electron gas in a high magnetic field displays macroscopically degenerate Landau levels, which can be split into Hofstadter subbands by means of a weak periodic potential. By carefully engineering such a potential, one can…
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the…
The ongoing need for effective epidemic modeling has driven advancements in capturing the complex dynamics of infectious diseases. Traditional models, such as Susceptible-Infected-Recovered, and graph-based approaches often fail to account…