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We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Data Analysis, Statistics and Probability · Physics 2018-12-05 Vsevolod Salnikov , Daniele Cassese , Renaud Lambiotte

How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum…

Machine Learning · Computer Science 2019-01-15 Xiao Dong , Ling Zhou

The acknowledged model for networks of collaborations is the hypergraph model. Nonetheless when it comes to be visualized hypergraphs are transformed into simple graphs. Very often, the transformation is made by clique expansion of the…

Social and Information Networks · Computer Science 2017-07-04 Xavier Ouvrard , Jean-Marie Le Goff , Stéphane Marchand-Maillet

Multivariate graphs are prolific across many fields, including transportation and neuroscience. A key task in graph analysis is the exploration of connectivity, to, for example, analyze how signals flow through neurons, or to explore how…

Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…

Social and Information Networks · Computer Science 2020-04-30 Joao Pita Costa , Tihana Galinac Grbac

Multilayer relationships among entities and information about entities must be accompanied by the means to analyze, visualize, and obtain insights from such data. We present open-source software (muxViz) that contains a collection of…

Physics and Society · Physics 2015-06-15 Manlio De Domenico , Mason A. Porter , Alex Arenas

Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high…

Social and Information Networks · Computer Science 2018-07-05 Christian Schulz

This paper describes TOBY, a visualization tool that helps a user explore the contents of an academic survey paper. The visualization consists of four components: a hierarchical view of taxonomic data in the survey, a document similarity…

For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…

History and Overview · Mathematics 2025-03-27 Fei Ma , Bing Yao

This article discusses how concepts and methods of complex networks can be applied to real-time imaging and computer vision. After a brief introduction of complex networks basic concepts, their use as means to represent and characterize…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 Luciano da Fontoura Costa

Graph theory provides a primary tool for analyzing and designing computer communication networks. In the past few decades, Graph theory has been used to study various types of networks, including the Internet, wide Area Networks, Local Area…

Networking and Internet Architecture · Computer Science 2009-07-20 Kamal Ahmat

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

Graphics · Computer Science 2024-07-30 Peter Oliver , Eugene Zhang , Yue Zhang

It is an increasingly common practice in several natural and social sciences to rely on network visualisations both as heuristic tools to get a first overview of relational datasets and as a way to offer an illustration of network analysis…

Physics and Society · Physics 2019-05-08 Tommaso Venturini , Mathieu Jacomy , Pablo Jensen

Visually mining a large influence graph is appealing yet challenging. People are amazed by pictures of newscasting graph on Twitter, engaged by hidden citation networks in academics, nevertheless often troubled by the unpleasant readability…

Social and Information Networks · Computer Science 2016-11-17 Lei Shi , Hanghang Tong , Jie Tang , Chuang Lin

Network clustering requires making many decisions manually, such as the number of groups and a statistical model to be used. Even after filtering using an information criterion or regularizing with a nonparametric framework, we are commonly…

Social and Information Networks · Computer Science 2019-06-05 Chihiro Noguchi , Tatsuro Kawamoto

Network visualization allows a quick glance at how nodes (or actors) are connected by edges (or ties). A conventional network diagram of "contact tree" maps out a root and branches that represent the structure of nodes and edges, often…

Social and Information Networks · Computer Science 2014-11-04 Arnaud Sallaberry , Yang-Chih Fu , Hwai-Chung Ho , Kwan-Liu Ma

We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…

Human-Computer Interaction · Computer Science 2021-04-23 Youjia Zhou , Archit Rathore , Emilie Purvine , Bei Wang

The aim of visualization is to support people in dealing with large and complex information structures, to make these structures more comprehensible, facilitate exploration, and enable knowledge discovery. However, users often have problems…

Human-Computer Interaction · Computer Science 2022-03-22 Christina Stoiber , Markus Wagner , Florian Grassinger , Margit Pohl , Holger Stitz , Marc Streit , Benjamin Potzmann , Wolfgang Aigner

Several graph visualization tools exist. However, they are not able to handle large graphs, and/or they do not allow interaction. We are interested on large graphs, with hundreds of thousands of nodes. Such graphs bring two challenges: the…

Social and Information Networks · Computer Science 2015-06-15 Jose Rodrigues , Hanghang Tong , Agma Traina , Christos Faloutsos , Jure Leskovec

Complex network topology might get pretty complicated challenging many network analysis objectives, such as community detection for example. This however makes common emergent network phenomena such as scale-free topology or small-world…

Social and Information Networks · Computer Science 2018-06-12 Stanislav Sobolevsky