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The co-occurrence association is widely observed in many empirical data. Mining the information in co-occurrence data is essential for advancing our understanding of systems such as social networks, ecosystem, and brain network. Measuring…

Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…

Proximity measures on graphs have a variety of applications in network analysis, including community detection. Previously they have been mainly studied in the context of networks without attributes. If node attributes are taken into…

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical…

We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…

We consider an index model of dyadic link formation with a homophily effect index and a degree heterogeneity index. We provide nonparametric identification results in a single large network setting for the potentially nonparametric…

Communities typically capture homophily as people of the same community share many common features. This paper is motivated by the problem of community detection in social networks, as it can help improve our understanding of the network…

Graph Convolutional Network (GCN) has shown remarkable potential of exploring graph representation. However, the GCN aggregating mechanism fails to generalize to networks with heterophily where most nodes have neighbors from different…

Graph Neural Networks (GNNs) have been predominant for graph learning tasks; however, recent studies showed that a well-known graph algorithm, Label Propagation (LP), combined with a shallow neural network can achieve comparable performance…

Despite the tremendous success of graph-based learning systems in handling structural data, it has been widely investigated that they are fragile to adversarial attacks on homophilic graph data, where adversaries maliciously modify the…

Graph Neural Networks (GNNs) have achieved significant success in various learning tasks on graph-structured data. Nevertheless, most GNNs struggle to generalize to heterophilic neighborhoods. Additionally, many GNNs ignore the directional…

The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…

Graph neural networks (GNNs) have emerged as a powerful tool for modeling graph-structured data. However, existing GNNs often struggle with heterophilic graphs, where connected nodes tend to have dissimilar features or labels. While…

Nestedness is a property of interaction networks widely observed in natural mutualistic communities. Despite a widespread interest on this pattern, no general consensus exists on how to measure it. Instead, several metrics aiming at…

Graph Convolutional Networks (GCNs) gained traction for graph representation learning, with recent attention on improving performance on heterophilic graphs for various real-world applications. The localized feature aggregation in a typical…

In recent years, Graph Neural Networks has received enormous attention from academia for its huge potential of modeling the network traits such as macrostructure and single node attributes. However, prior mainstream works mainly focus on…

Graph Convolutional Networks (GCNs) are predominantly tailored for graphs displaying homophily, where similar nodes connect, but often fail on heterophilic graphs. The strategy of adopting distinct approaches to learn from homophilic and…

Real-world social networks often exhibit high levels of clustering, positive degree assortativity, short average path lengths (small-world property) and right-skewed but rarely power law degree distributions. On the other hand homophily,…

Homophily based on observables is widespread in networks. Therefore, homophily based on unobservables (fixed effects) is also likely to be an important determinant of the interaction outcomes. Failing to properly account for latent…

While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…