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Subgraph counting is a fundamental task that underpins several network analysis methodologies, including community detection and graph two-sample tests. Counting subgraphs is a computationally intensive problem. Substantial research has…

Combinatorics · Mathematics 2025-11-19 Feng Yu , Mingao Yuan

Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…

Machine Learning · Computer Science 2021-02-03 Xue Liu , Wei Wei , Xiangnan Feng , Xiaobo Cao , Dan Sun

Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…

Computation · Statistics 2015-06-04 Rohan Shah , Dirk P. Kroese

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Statistics Theory · Mathematics 2021-04-21 Anatol E. Wegner , Sofia Olhede

We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…

Combinatorics · Mathematics 2026-05-11 Sasha Bell , Serte Donderwinkel , Remco van der Hofstad

Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…

Statistics Theory · Mathematics 2026-01-21 Dong Huang , Pengkun Yang

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

Social and Information Networks · Computer Science 2024-04-18 Radosław Nowak , Adam Małkowski , Daniel Cieślak , Piotr Sokół , Paweł Wawrzyński

Assessing homophily in large-scale networks is central to understanding structural regularities in graphs, and thus inform the choice of models (such as graph neural networks) adopted to learn from network data. Evaluation of smoothness…

Signal Processing · Electrical Eng. & Systems 2025-12-22 Hamed Ajorlou , Gonzalo Mateos , Luana Ruiz

We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…

We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…

Discrete Mathematics · Computer Science 2012-11-06 Ajit Diwan , Soumitra Pal , Abhiram Ranade

Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two…

Machine Learning · Computer Science 2018-10-09 Xutong Liu , Yu-Zhen Janice Chen , John C. S. Lui , Konstantin Avrachenkov

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…

Statistical Mechanics · Physics 2009-11-10 Bo Söderberg

We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by…

Machine Learning · Computer Science 2014-05-20 Akshay Gadde , Aamir Anis , Antonio Ortega

This work concerns sampling of smooth signals on arbitrary graphs. We first study a structured sampling strategy for such smooth graph signals that consists of a random selection of few pre-defined groups of nodes. The number of groups to…

Social and Information Networks · Computer Science 2017-05-08 Gilles Puy , Patrick Pérez

This paper is concerned by the problem of selecting an optimal sampling set of sensors over a network of time series for the purpose of signal recovery at non-observed sensors with a minimal reconstruction error. The problem is motivated by…

Machine Learning · Statistics 2020-04-27 Yiye Jiang , Jérémie Bigot , Sofian Maabout

Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, it is today possible to produce and analyze social and biological networks with detailed information on the time of occurrence and…

Physics and Society · Physics 2012-04-17 V. Nicosia , J. Tang , M. Musolesi , G. Russo , C. Mascolo , V. Latora

Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical…

Signal Processing · Electrical Eng. & Systems 2019-11-20 Junhao Yu , Xuan Xie , Hui Feng , Bo Hu

There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…

Machine Learning · Statistics 2022-08-05 Florence Regol , Soumyasundar Pal , Jianing Sun , Yingxue Zhang , Yanhui Geng , Mark Coates

This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…

Machine Learning · Computer Science 2021-10-04 Shahana Ibrahim , Xiao Fu

We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…

Combinatorics · Mathematics 2023-03-06 Audace A. V. Dossou-Olory