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Algorithms 2017, 10(1), 1; doi:10.3390/a10010001

MultiAspect Graphs: Algebraic Representation and Algorithms

1
National Laboratory for Scientific Computing (LNCC), Av. Getúlio Vargas 333, 25651-075 Petrópolis, Brazil
2
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
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)
View Full-Text   |   Download PDF [778 KB, uploaded 26 December 2016]   |  

Abstract

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
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MDPI and ACS Style

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

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