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Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…

Disordered Systems and Neural Networks · Physics 2007-05-23 Alexander K. Hartmann , Martin Weigt

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Signal Processing · Electrical Eng. & Systems 2025-12-12 Gonzalo Mateos , Yanning Shen , Georgios B. Giannakis , Ananthram Swami

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…

Physics and Society · Physics 2010-09-17 Santo Fortunato

Graph learning plays a pivotal role and has gained significant attention in various application scenarios, from social network analysis to recommendation systems, for its effectiveness in modeling complex data relations represented by graph…

Machine Learning · Computer Science 2024-03-08 Man Wu , Xin Zheng , Qin Zhang , Xiao Shen , Xiong Luo , Xingquan Zhu , Shirui Pan

Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…

Machine Learning · Computer Science 2020-07-15 Natalia Vesselinova , Rebecca Steinert , Daniel F. Perez-Ramirez , Magnus Boman

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…

Social and Information Networks · Computer Science 2017-10-12 Matthieu Latapy , Tiphaine Viard , Clémence Magnien

Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of…

Social and Information Networks · Computer Science 2019-08-22 Palash Goyal , Emilio Ferrara

Given a time-evolving network, how can we detect communities over periods of high internal and low external interactions? To address this question we generalize traditional local community detection in graphs to the setting of dynamic…

Social and Information Networks · Computer Science 2017-09-14 Daniel J. DiTursi , Gaurav Ghosh , Petko Bogdanov

The abundance of interconnected data has fueled the design and implementation of graph generators reproducing real-world linking properties, or gauging the effectiveness of graph algorithms, techniques and applications manipulating these…

Databases · Computer Science 2020-01-23 Angela Bonifati , Irena Holubová , Arnau Prat-Pérez , Sherif Sakr

Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually…

Machine Learning · Computer Science 2018-11-07 Yao Ma , Ziyi Guo , Zhaochun Ren , Eric Zhao , Jiliang Tang , Dawei Yin

Many real-world graphs or networks are temporal, e.g., in a social network persons only interact at specific points in time. This information directs dissemination processes on the network, such as the spread of rumors, fake news, or…

Social and Information Networks · Computer Science 2021-08-23 Lutz Oettershagen , Nils M. Kriege , Christopher Morris , Petra Mutzel

Graph-structured data are pervasive in the real-world such as social networks, molecular graphs and transaction networks. Graph neural networks (GNNs) have achieved great success in representation learning on graphs, facilitating various…

Machine Learning · Computer Science 2025-02-27 Zhimeng Guo , Teng Xiao , Zongyu Wu , Charu Aggarwal , Hui Liu , Suhang Wang

Social network analysis is a popular discipline among the social and behavioural sciences, in which the relationships between different social entities are modelled as a network. One of the most popular problems in social network analysis…

Social and Information Networks · Computer Science 2022-08-30 Javier Fumanal-Idocin , Oscar Cordón , María Minárová , Amparo Alonso-Betanzos , Humberto Bustince

Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-02 Davide Rucci , Emanuele Carlini , Patrizio Dazzi , Hanna Kavalionak , Matteo Mordacchini

Graph models help understand network dynamics and evolution. Creating graphs with controlled topology and embedded partitions is a common strategy for evaluating community detection algorithms. However, existing benchmarks often overlook…

Social and Information Networks · Computer Science 2025-10-09 Laurent Brisson , Cécile Bothorel , Nicolas Duminy

Graph-based analyses have gained a lot of relevance in the past years due to their high potential in describing complex systems by detailing the actors involved, their relations and their behaviours. Nevertheless, in scenarios where these…

Machine Learning · Computer Science 2021-06-11 Francesco Zola , Lander Segurola , Jan Lukas Bruse , Mikel Galar Idoate

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…

Machine Learning · Computer Science 2024-01-17 Sanaz Hasanzadeh Fard

Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…

Machine Learning · Computer Science 2024-08-21 Victor-Alexandru Darvariu , Stephen Hailes , Mirco Musolesi

Community detection is an important tool for analyzing the social graph of mobile phone users. The problem of finding communities in static graphs has been widely studied. However, since mobile social networks evolve over time, static graph…

Social and Information Networks · Computer Science 2013-12-04 Carlos Sarraute , Gervasio Calderon

Many algorithms have been proposed in the last ten years for the discovery of dynamic communities. However, these methods are seldom compared between themselves. In this article, we propose a generator of dynamic graphs with planted…

Social and Information Networks · Computer Science 2020-07-20 Remy Cazabet , Souaad Boudebza , Giulio Rossetti