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Clustering analysis has been widely used in trust evaluation on various complex networks such as wireless sensors networks and online social networks. Spectral clustering is one of the most commonly used algorithms for graph-structured data…

Graph modification problems are computational tasks where the goal is to change an input graph $G$ using operations from a fixed set, in order to make the resulting graph satisfy a target property, which usually entails membership to a…

Centrality metrics have been widely applied to identify the nodes in a graph whose removal is effective in decomposing the graph into smaller sub-components. The node--removal process is generally used to test network robustness against…

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…

In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the…

To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an…

Graph Neural Networks (GNNs) have led to state-of-the-art performance on a variety of machine learning tasks such as recommendation, node classification and link prediction. Graph neural network models generate node embeddings by merging…

Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the…

In recent years, graph neural networks (GNNs) have become increasingly popular for solving NP-hard combinatorial optimization (CO) problems, such as maximum cut and maximum independent set. The core idea behind these methods is to represent…

Decomposing hypergraphs is a key task in hypergraph analysis with broad applications in community detection, pattern discovery, and task scheduling. Existing approaches such as $k$-core and neighbor-$k$-core rely on vertex degree…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

This paper studies semi-supervised graph classification, which is an important problem with various applications in social network analysis and bioinformatics. This problem is typically solved by using graph neural networks (GNNs), which…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of…

This paper introduces a new problem in the field of graph mining and social network analysis called new node prediction. More technically, the task can be categorized as zero-shot out-of-graph all-links prediction. This challenging problem…

Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or sub-graph) detection within a…

Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…

The fundamental principle of Graph Neural Networks (GNNs) is to exploit the structural information of the data by aggregating the neighboring nodes using a `graph convolution' in conjunction with a suitable choice for the network…

Degree distributions are arguably the most important property of real world networks. The classic edge configuration model or Chung-Lu model can generate an undirected graph with any desired degree distribution. This serves as a good null…

We study the problem of semi-supervised learning on graphs, for which graph neural networks (GNNs) have been extensively explored. However, most existing GNNs inherently suffer from the limitations of over-smoothing, non-robustness, and…