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Enhancing multiplex global efficiency.
- Source :
- Numerical Algorithms; May2024, Vol. 96 Issue 1, p397-416, 20p
- Publication Year :
- 2024
-
Abstract
- Modeling complex systems that consist of different types of objects leads to multilayer networks, in which vertices are connected by both inter-layer and intra-layer edges. In this paper, we investigate multiplex networks, in which vertices in different layers are identified with each other, and the only inter-layer edges are those that connect a vertex with its copy in other layers. Let the third-order adjacency tensor A ∈ R N × N × L and the parameter γ ≥ 0 , which is associated with the ease of communication between layers, represent a multiplex network with N vertices and L layers. To measure the ease of communication in a multiplex network, we focus on the average inverse geodesic length, which we refer to as the multiplex global efficiency e A (γ) by means of the multiplex path length matrix P ∈ R N × N . This paper generalizes the approach proposed in [15] for single-layer networks. We describe an algorithm based on min-plus matrix multiplication to construct P, as well as variants P K that only take into account multiplex paths made up of at most K intra-layer edges. These matrices are applied to detect redundant edges and to determine non-decreasing lower bounds e A K (γ) for e A (γ) , for K = 1 , 2 , ⋯ , N - 2 . Finally, the sensitivity of e A K (γ) to changes of the entries of the adjacency tensor A is investigated to determine edges that should be strengthened to enhance the multiplex global efficiency the most. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATRIX multiplications
TELECOMMUNICATION systems
Subjects
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 96
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 176465339
- Full Text :
- https://doi.org/10.1007/s11075-023-01651-5