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With the impressive growth of network models in practically every scientific and technological area, we are often faced with the need to compare graphs, i.e., to quantify their (dis)similarity using appropriate metrics. This is necessary,…

Social and Information Networks · Computer Science 2025-07-03 Carlo Piccardi

In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…

Discrete Mathematics · Computer Science 2025-12-10 Pierre Miasnikof , Alexander Y. Shetopaloff

The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…

Social and Information Networks · Computer Science 2014-07-23 Sadegh Aliakbary , Jafar Habibi , Ali Movaghar

Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…

Computation · Statistics 2022-06-28 Pierre Miasnikof , Alexander Y. Shestopaloff , Cristián Bravo , Yuri Lawryshyn

As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is…

Social and Information Networks · Computer Science 2019-07-26 James P. Bagrow , Erik M. Bollt

Identifying and quantifying structural dissimilarities between complex networks is a fundamental and challenging problem in network science. Previous network comparison methods are based on the structural features, such as the length of…

Social and Information Networks · Computer Science 2021-11-29 Zhipeng Wang , Xiu-Xiu Zhan , Chuang Liu , Zi-Ke Zhang

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…

Social and Information Networks · Computer Science 2014-06-23 Matthieu Roy , Stefan Schmid , Gilles Trédan

Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Previously, most network comparison methods that rely on topological properties have been restricted to measuring…

Physics and Society · Physics 2024-01-15 Chenwei Xie , Qiao Ke , Haoyu Chen , Chuang Liu , Xiu-Xiu Zhan

The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different…

Physics and Society · Physics 2011-03-30 Kathryn Cooper , Mauricio Barahona

Networks are widely used to model real-world systems and uncover their topological features. Network properties such as the degree distribution and shortest path length have been computed in numerous real-world networks, and most of them…

Social and Information Networks · Computer Science 2017-07-17 David Aparício , Pedro Ribeiro , Fernando Silva

Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…

Social and Information Networks · Computer Science 2018-07-26 Leo Torres , Pablo Suarez-Serrato , Tina Eliassi-Rad

A wide range of tasks in network analysis, such as clustering network populations or identifying anomalies in temporal graph streams, require a measure of the similarity between two graphs. To provide a meaningful data summary for…

Physics and Society · Physics 2024-10-15 Helcio Felippe , Federico Battiston , Alec Kirkley

Networks are fundamental to the study of complex systems, ranging from social contacts, message transactions, to biological regulations and economical networks. In many realistic applications, these networks may vary over time. Modeling and…

Social and Information Networks · Computer Science 2020-04-07 Kun Tu , Jian Li , Don Towsley , Dave Braines , Liam Turner

Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…

Discrete Mathematics · Computer Science 2022-07-04 Timo Gervens , Martin Grohe

The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…

Social and Information Networks · Computer Science 2013-12-24 Sadegh Aliakbary , Jafar Habibi , Ali Movaghar

Quantifying the similarity between two networks is critical in many applications. A number of algorithms have been proposed to compute graph similarity, mainly based on the properties of nodes and edges. Interestingly, most of these…

Neurons and Cognition · Quantitative Biology 2017-09-22 Ahmad Mheich , Mahmoud Hassan , Mohamad Khalil , Vincent Gripon , Olivier Dufor , Fabrice Wendling

Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…

Combinatorics · Mathematics 2025-09-30 Matthias Dehmer , Izudin Redžepović , Niko Tratnik , Petra Žigert Pleteršek

Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…

Social and Information Networks · Computer Science 2013-07-16 Sadegh Aliakbary , Sadegh Motallebi , Jafar Habibi , Ali Movaghar

This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…

Social and Information Networks · Computer Science 2016-01-20 Weiyu Huang , Alejandro Ribeiro

Network comparison is a widely-used tool for analyzing complex systems, with applications in varied domains including comparison of protein interactions or highlighting changes in structure of trade networks. In recent years, a number of…

Social and Information Networks · Computer Science 2023-03-09 Miguel E. P. Silva , Robert E. Gaunt , Luis Ospina-Forero , Caroline Jay , Thomas House
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