Paper Info
Title
MultiAspect Graphs: Algebraic representation and algorithms.
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.
Year
DOI
Venue
2015
10.3390/a10010001
ALGORITHMS
Keywords
Field
DocType
complex network,multilayer network,time-varying network,high order network,graph algorithms
Matrix (mathematics),Computer science,Theoretical computer science,Artificial intelligence,Complex network,Algebra representation,Graph,Mathematical optimization,Breadth-first search,Algorithm,Directed graph,Isomorphism,Python (programming language),Machine learning
Journal
Volume
Issue
Citations 
10
1
13
PageRank 
References 
Authors
0.53
18
3
Name
Order
Citations
PageRank
Klaus Wehmuth17010.17
Eric Fleury225225.08
Artur Ziviani364656.62