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Graph theory provides a powerful framework to investigate brain functional connectivity networks and their modular organization. However, most graph-based methods suffer from a fundamental resolution limit that may have affected previous…

The successful integration of graph neural networks into recommender systems (RSs) has led to a novel paradigm in collaborative filtering (CF), graph collaborative filtering (graph CF). By representing user-item data as an undirected,…

Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…

The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…

Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…

Generalizing to unseen graph tasks without task-specific supervision is challenging: conventional graph neural networks are typically tied to a fixed label space, while large language models (LLMs) struggle to capture graph structure. We…

Testing whether two graphs come from the same distribution is of interest in many real world scenarios, including brain network analysis. Under the random dot product graph model, the nonparametric hypothesis testing frame-work consists of…

Sampling graph colorings via local Markov chains is a central problem in approximate counting and Markov chain Monte Carlo (MCMC). We address the problem of sampling a random $k$-coloring of a graph with maximum degree $\Delta$. The…

Identifying the connected components of a graph, apart from being a fundamental problem with countless applications, is a key primitive for many other algorithms. In this paper, we consider this problem in parallel settings. Particularly,…

An increasingly important brain function analysis modality is functional connectivity analysis which regards connections as statistical codependency between the signals of different brain regions. Graph-based analysis of brain connectivity…

Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional…

Persistent homology is a fundamental tool in topological data analysis; however, it lacks methods to quantify the fragility or fineness of cycles, anticipate their formation or disappearance, or evaluate their stability beyond persistence.…

Much data with graph structures satisfy the principle of homophily, meaning that connected nodes tend to be similar with respect to a specific attribute. As such, ubiquitous datasets for graph machine learning tasks have generally been…

Graph neural network (GNN) has shown convincing performance in learning powerful node representations that preserve both node attributes and graph structural information. However, many GNNs encounter problems in effectiveness and efficiency…

We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…

Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (iid). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of…

An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among…

Objective: Modelling the associations from high-throughput experimental molecular data has provided unprecedented insights into biological pathways and signalling mechanisms. Graphical models and networks have especially proven to be useful…

In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…