Extending the Adapted PageRank Algorithm Centrality to Multiplex Networks with Data Using the PageRank Two-Layer Approach
Abstract
:1. Introduction
1.1. Literature Review
1.2. Main Contribution
1.3. Structure of the Paper
2. Methodology
2.1. The Adapted PageRank Algorithm (APA) Model
- It is nonnegative.
- It is stochastic by columns.
- The highest eigenvalue of P is .
Algorithm 1: (Adapted PageRank algorithm (APA)). Let be a primary graph representing a network with n nodes. |
|
2.2. The Biplex Approach for Classic PageRank
- , physical layer, it is the network G.
- , teleportation layer, it is an all-to-all network, with weights given by the personalized vector.
2.3. Constructing the APABI Centrality by Applying the Two-Layer Approach
Algorithm 2: (Adapted PageRank algorithm biplex (APABI)). Let , with layers and adjacency matrices be a biplex network with n nodes. |
|
2.4. A Note about the Computational Cost
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
APA | Adapted PageRank algorithm |
APABI | Adapted PageRank algorithm biplex |
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Node | Social Networks Links | Messages | Game Links | Games |
---|---|---|---|---|
1 | 15 | 33 | ||
2 | 9 | 26 | ||
3 | 12 | 18 | ||
4 | 19 | 32 | ||
5 | 28 | 20 | ||
6 | 7 | 12 | ||
7 | 20 | 32 | ||
8 | 7 | 6 | ||
9 | 16 | 18 | ||
10 | 21 | 25 | ||
11 | 14 | 24 | ||
12 | 8 | 18 | ||
13 | 11 | 6 | ||
14 | 13 | 26 | ||
15 | 11 | 38 | ||
16 | 14 | 6 | ||
17 | 12 | 12 | ||
18 | 35 | 30 | ||
19 | 15 | 8 | ||
20 | 27 | 25 |
Node | APA Layer | APA Layer | APABI | |||
---|---|---|---|---|---|---|
Centrality | Ranking | Centrality | Ranking | Centrality | Ranking | |
1 | 0.05025 | 7 | 0.06394 | 3 | 0.05581 | 7 |
2 | 0.03110 | 17 | 0.04635 | 13 | 0.03777 | 16 |
3 | 0.04063 | 13 | 0.04330 | 14 | 0.04193 | 13 |
4 | 0.04891 | 9 | 0.08152 | 1 | 0.06517 | 3 |
5 | 0.07731 | 3 | 0.05134 | 9 | 0.06440 | 5 |
6 | 0.02494 | 20 | 0.03356 | 18 | 0.02862 | 20 |
7 | 0.06157 | 5 | 0.06867 | 2 | 0.06477 | 4 |
8 | 0.02791 | 19 | 0.03133 | 19 | 0.03071 | 19 |
9 | 0.05481 | 6 | 0.03965 | 15 | 0.04836 | 11 |
10 | 0.06530 | 4 | 0.05433 | 7 | 0.05902 | 6 |
11 | 0.04936 | 8 | 0.05341 | 8 | 0.05013 | 9 |
12 | 0.02852 | 18 | 0.04671 | 12 | 0.03727 | 17 |
13 | 0.03626 | 16 | 0.03407 | 17 | 0.03684 | 18 |
14 | 0.04776 | 10 | 0.05047 | 10 | 0.04820 | 12 |
15 | 0.03902 | 15 | 0.06387 | 4 | 0.05085 | 8 |
16 | 0.04550 | 12 | 0.02807 | 20 | 0.03781 | 15 |
17 | 0.04020 | 14 | 0.03830 | 16 | 0.04033 | 14 |
18 | 0.09182 | 2 | 0.06305 | 5 | 0.07590 | 2 |
19 | 0.04700 | 11 | 0.04686 | 11 | 0.04838 | 10 |
20 | 0.09186 | 1 | 0.06111 | 6 | 0.07775 | 1 |
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Share and Cite
Agryzkov, T.; Curado, M.; Pedroche, F.; Tortosa, L.; Vicent, J.F. Extending the Adapted PageRank Algorithm Centrality to Multiplex Networks with Data Using the PageRank Two-Layer Approach. Symmetry 2019, 11, 284. https://doi.org/10.3390/sym11020284
Agryzkov T, Curado M, Pedroche F, Tortosa L, Vicent JF. Extending the Adapted PageRank Algorithm Centrality to Multiplex Networks with Data Using the PageRank Two-Layer Approach. Symmetry. 2019; 11(2):284. https://doi.org/10.3390/sym11020284
Chicago/Turabian StyleAgryzkov, Taras, Manuel Curado, Francisco Pedroche, Leandro Tortosa, and José F. Vicent. 2019. "Extending the Adapted PageRank Algorithm Centrality to Multiplex Networks with Data Using the PageRank Two-Layer Approach" Symmetry 11, no. 2: 284. https://doi.org/10.3390/sym11020284