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A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree.…

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…

Large language models (LLMs) show promising performance on small-scale graph reasoning tasks but fail when handling real-world graphs with complex queries. This phenomenon arises from LLMs' working memory constraints, which result in their…

Graph pattern mining (GPM) is an important application that identifies structures from graphs. Despite the recent progress, the performance gap between the state-of-the-art GPM systems and an efficient algorithm--pattern decomposition--is…

With a core-periphery structure of networks, core nodes are densely interconnected, peripheral nodes are connected to core nodes to different extents, and peripheral nodes are sparsely interconnected. Core-periphery structure composed of a…

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…

Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally…

In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential…

We show how to find and efficiently maintain maximal k-edge-connected subgraphs in undirected graphs. In particular, we provide the following results. (1) A general framework for maintaining the maximal k-edge-connected subgraphs upon…

Finding dense subgraphs is a core problem in graph mining with many applications in diverse domains. At the same time many real-world networks vary over time, that is, the dataset can be represented as a sequence of graph snapshots. Hence,…

As the use of MultiLayer Networks (or MLNs) for modeling and analysis is gaining popularity, it is becoming increasingly important to propose a community definition that encompasses the multiple features represented by MLNs and develop…

With the development of complex networks, many researchers have paid greater attention to studying the control of complex networks over the last decade. Although some theoretical breakthroughs allow us to identify all driver nodes, we still…

Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final…

The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…

How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…

Despite the advances in large language models (LLMs), how they use their knowledge for reasoning is not yet well understood. In this study, we propose a method that deconstructs complex real-world questions into a graph, representing each…

Graph representation learning has many real-world applications, from super-resolution imaging, 3D computer vision to drug repurposing, protein classification, social networks analysis. An adequate representation of graph data is vital to…

A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…

Graph classification is a pivotal challenge in machine learning, especially within the realm of graph-based data, given its importance in numerous real-world applications such as social network analysis, recommendation systems, and…