A Novel Method to Rank Influential Nodes in Complex Networks Based on Tsallis Entropy
Abstract
:1. Introduction
2. Related Works
3. Motivation and Proposed Approach
3.1. Tsallis Entropy
3.2. TsallisRank
3.2.1. Parameter Computing
- Calculate compactness centrality
- Calculate the Tsallis parameters
- Calculating the probability set
- Neighbor entropy
3.2.2. Coreness Centrality
- Ability to calculate the impact
- Computing the neighborhood core
- TsallisRank
3.3. Algorithm Description
Algorithm 1: TRank algorithm. |
Input: Network G(V,E) Output: TRank Value for each node 1. Find neighboring nodes of node 2. Compute for node 3. For node in do 4. compute ratio1 = degree ()/sum(degree(all neighbors of )) 5. = (pow(ratio1,) − ratio1)/(1-) 6. End For 7. For node in do 8. compute second_neighbor_degree= the degree of the second neighbor for node 9. compute ratio2 = sum(degree(all neighbors of ))/sum(second_neighbor_degree()) 10. = (pow(ratio2,) − ratio2)/(1-) 11. End For 12. compute 13. For node in do 14. = sum() 15. End For 16. For node in do 17. = sum(SI) 18. End For |
4. Experiment
4.1. Network Datasets
4.2. TsallisRank Algorithm Recognition Analysis
- D method
- CCDF method
- M method
- Jaccard similarity coefficient
4.3. Algorithm Correctness
4.4. Algorithm Efficiency
5. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Network | |V| | |E| | Average Degree | Maximum Degree | Assortativity | Clustering Coefficient |
---|---|---|---|---|---|---|
BAG_400_200 | 400 | 40,000 | 200.0 | 384 | −0.398111 | 0.722654 |
BAG_600_300 | 600 | 90,000 | 300.0 | 577 | −0.397054 | 0.721492 |
BAG_800_400 | 800 | 160,000 | 400.0 | 776 | −0.397650 | 0.724718 |
BAG_1000_500 | 1000 | 250,000 | 500.0 | 967 | −0.397126 | 0.722987 |
BAG_1200_600 | 1200 | 360,000 | 600.0 | 1159 | −0.397411 | 0.723613 |
BAG_1400_700 | 1400 | 490,000 | 700.0 | 1347 | −0.397143 | 0.723255 |
FPA_acyclic_f_1_BA_model | 100,006 | 100,005 | 1.99998 | 1340 | −0.014383 | 0.0 |
FPA_acyclic_f_07 | 100,006 | 100,005 | 1.99998 | 1621 | −0.028993 | 0.0 |
FPA_acyclic_f_05 | 100,006 | 100,005 | 1.99998 | 4981 | −0.047784 | 0.0 |
FPA_acyclic_f_02 | 100,006 | 100,005 | 1.99998 | 21,951 | −0.157886 | 0.0 |
Network | |V| | |E| | Average Degree | Maximum Degree | Assortativity | Clustering Coefficient |
---|---|---|---|---|---|---|
Karate | 34 | 78 | 4.588 | 17 | −0.4756 | 0.5706 |
Dolphins | 62 | 159 | 5.129 | 12 | −0.043594 | 0.2590 |
Jazz | 198 | 2742 | 27.697 | 100 | 0.0202 | 0.6175 |
Elegans | 453 | 2025 | 8.940 | 237 | −0.2258 | 0.6465 |
1133 | 5451 | 9.622 | 71 | 0.0782 | 0.2203 | |
Euroroad | 1174 | 1417 | 2.414 | 10 | 0.1267 | 0.0167 |
Yeast | 2361 | 7182 | 6.0839 | 66 | −0.0846 | 0.1301 |
Hamsterster | 2426 | 16,631 | 13.711 | 273 | 0.0474 | 0.5376 |
PowerGrid | 4941 | 6594 | 2.669 | 273 | 0.0035 | 0.0801 |
PGP | 10,680 | 24,316 | 4.554 | 205 | 0.2382 | 0.2659 |
Network | D(DC) | D(Ks) | D(LE) | D(MDD) | D(Cnc+) | D(TRank) |
---|---|---|---|---|---|---|
Karate | 0.3235 | 0.1471 | 0.8235 | 0.4412 | 0.7647 | 0.7941 |
Dolphins | 0.1935 | 0.0968 | 0.9194 | 0.4032 | 0.8871 | 0.9677 |
Jazz | 0.3131 | 0.1869 | 0.9646 | 0.6768 | 0.9646 | 0.9697 |
Elegans | 0.0883 | 0.0574 | 0.8366 | 0.1987 | 0.8676 | 0.9029 |
0.0424 | 0.0477 | 0.8914 | 0.1703 | 0.9170 | 0.9762 | |
Euroroad | 0.0077 | 0.0068 | 0.1806 | 0.0187 | 0.0707 | 0.9446 |
Yeast | 0.0237 | 0.0216 | 0.6357 | 0.0923 | 0.6192 | 0.7954 |
Hamsterster | 0.0458 | 0.0528 | 0.6587 | 0.1620 | 0.6686 | 0.7003 |
PowerGrid | 0.0032 | 0.0040 | 0.2117 | 0.0105 | 0.0565 | 0.9041 |
PGP | 0.0078 | 0.0124 | 0.3727 | 0.0329 | 0.2902 | 0.7456 |
Network | M(DC) | M(Ks) | M(LE) | M(MDD) | M(Cnc+) | M(TRank) |
---|---|---|---|---|---|---|
Karate | 0.7079 | 0.5499 | 0.9577 | 0.7536 | 0.9472 | 0.9542 |
Dolphins | 0.8312 | 0.5576 | 0.9905 | 0.9091 | 0.9895 | 0.9979 |
Jazz | 0.9659 | 0.8951 | 0.9993 | 0.9911 | 0.9993 | 0.9994 |
Elegans | 0.7922 | 0.7399 | 0.9972 | 0.8768 | 0.9980 | 0.9988 |
0.8874 | 0.8521 | 0.9990 | 0.9233 | 0.9997 | 0.9999 | |
Euroroad | 0.4442 | 0.3312 | 0.9181 | 0.6510 | 0.9463 | 0.9990 |
Yeast | 0.7472 | 0.7052 | 0.9921 | 0.7477 | 0.9962 | 0.9972 |
Hamsterster | 0.8980 | 0.8907 | 0.9853 | 0.9274 | 0.9856 | 0.9858 |
PowerGrid | 0.5927 | 0.3713 | 0.9635 | 0.6940 | 0.9568 | 0.9999 |
PGP | 0.6193 | 0.5000 | 0.9781 | 0.6679 | 0.9939 | 0.9997 |
Network | τ(σ,DC) | τ(σ,Ks) | τ(σ,LE) | τ(σ,MDD) | τ(σ,Cnc+) | τ(σ, TRank) | ||
---|---|---|---|---|---|---|---|---|
Karate | 0.250 | 0.129 | 0.6310 | 0.5490 | 0.6542 | 0.6542 | 0.9269 | 0.8128 |
Dolphins | 0.150 | 0.147 | 0.7805 | 0.5796 | 0.7689 | 0.8170 | 0.8403 | 0.9418 |
Jazz | 0.040 | 0.026 | 0.8371 | 0.7847 | 0.8415 | 0.8663 | 0.9455 | 0.9726 |
Elegans | 0.050 | 0.025 | 0.6677 | 0.6931 | 0.5685 | 0.6902 | 0.8636 | 0.9199 |
0.050 | 0.054 | 0.7892 | 0.7962 | 0.7654 | 0.8073 | 0.9413 | 0.9578 | |
Euroroad | 0.275 | 0.333 | 0.5572 | 0.4571 | 0.4249 | 0.6721 | 0.8337 | 0.9341 |
Yeast | 0.100 | 0.061 | 0.5908 | 0.6147 | 0.5241 | 0.6490 | 0.9222 | 0.9289 |
Hamsterster | 0.020 | 0.024 | 0.7447 | 0.7333 | 0.6416 | 0.7510 | 0.9234 | 0.9349 |
PowerGrid | 0.200 | 0.258 | 0.6244 | 0.4503 | 0.5055 | 0.6667 | 0.7887 | 0.9107 |
PGP | 0.100 | 0.053 | 0.3644 | 0.3651 | 0.2026 | 0.3745 | 0.7840 | 0.6913 |
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Chen, X.; Zhou, J.; Liao, Z.; Liu, S.; Zhang, Y. A Novel Method to Rank Influential Nodes in Complex Networks Based on Tsallis Entropy. Entropy 2020, 22, 848. https://doi.org/10.3390/e22080848
Chen X, Zhou J, Liao Z, Liu S, Zhang Y. A Novel Method to Rank Influential Nodes in Complex Networks Based on Tsallis Entropy. Entropy. 2020; 22(8):848. https://doi.org/10.3390/e22080848
Chicago/Turabian StyleChen, Xuegong, Jie Zhou, Zhifang Liao, Shengzong Liu, and Yan Zhang. 2020. "A Novel Method to Rank Influential Nodes in Complex Networks Based on Tsallis Entropy" Entropy 22, no. 8: 848. https://doi.org/10.3390/e22080848