Next Article in Journal
A Pilot-Pattern Based Algorithm for MIMO-OFDM Channel Estimation
Previous Article in Journal
A Tensor Decomposition Based Multiway Structured Sparse SAR Imaging Algorithm with Kronecker Constraint
Previous Article in Special Issue
Utilizing Network Structure to Accelerate Markov Chain Monte Carlo Algorithms
Article Menu

Export Article

Open AccessArticle

MultiAspect Graphs: Algebraic Representation and Algorithms

National Laboratory for Scientific Computing (LNCC), Av. Getúlio Vargas 333, 25651-075 Petrópolis, Brazil
Institut national de recherche en informatique et en automatique (INRIA), Centre national de la recherche scientifique (CNRS), Université de Lyon, École normale supérieure de Lyon, UCB Lyon 1, LIP UMR 5668, F-69342, 46, Alleé d’Italie, 69364 Lyon, France
Authors to whom correspondence should be addressed.
Academic Editor: Natarajan Meghanathan
Algorithms 2017, 10(1), 1;
Received: 25 September 2016 / Revised: 12 December 2016 / Accepted: 19 December 2016 / Published: 25 December 2016
(This article belongs to the Special Issue Algorithms for Complex Network Analysis)
PDF [778 KB, uploaded 26 December 2016]


We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper. View Full-Text
Keywords: complex network; multilayer network; time-varying network; high order network; graph algorithms complex network; multilayer network; time-varying network; high order network; graph algorithms

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Wehmuth, K.; Fleury, É.; Ziviani, A. MultiAspect Graphs: Algebraic Representation and Algorithms. Algorithms 2017, 10, 1.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top