Identifying Influential Nodes in Complex Networks Based on Node Itself and Neighbor Layer Information
Abstract
:1. Introduction
2. Materials and Methods
2.1. Node Influence Based on Node and Neighbor Layer Information
Algorithm 1. The NINLp Method |
Input: the network G = (V, E) |
Output: node influence of NINLp centrality |
1: for i = 1 to |V| |
2: for j = 1 to |V| |
3: calculate the shortest path length between node i and node j |
4: end for |
5: end for |
6: calculate average path length L |
7: for i = 1 to |V| |
8: calculate the Degree centrality of node i |
9: end for |
10: for i = 1 to |V| |
11: find the neighbor nodes with a radius of ceil(L) from the node i |
12: calculate NINL0 of node i according to Equation (1) |
13: end for |
14: for i = 1 to |V| |
15: find the nearest neighbor nodes of node i |
16: end for |
17: set the value of p |
18: Recursively calculate NINLp centrality according to Equation (2) |
19: return NINLp centrality |
2.2. Benchmark Methods
2.2.1. Degree Centrality
2.2.2. Betweenness Centrality
2.2.3. Closeness Centrality
2.2.4. Density Centrality
2.2.5. Gravity Model
2.2.6. Clustered Local-Degree (CLD) Method
2.2.7. GLI Method
3. Experimental Data and Evaluation Criteria
3.1. Datasets
3.2. Spreading Model and Evaluation Criteria
3.2.1. SIR Model
3.2.2. CCDF Method
3.2.3. Kendall Correlation Coefficient
3.2.4. Jaccard Similarity Coefficient
4. Experiment and Analysis
4.1. Discrimination Experiment
4.2. Accuracy Experiment
4.2.1. Selection of p-Value
4.2.2. Influence Consistency Experiment
4.2.3. Recognition Effect of Each Method under a Certain Range of Propagation Probability
4.2.4. Recognition Effect of Each Method under a Certain Percentage of Ranking Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Node | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
NINL0 | 29 | 37 | 37 | 38 | 37 | 37 | 37 | 38 | 38 | 37 | 37 | 37 | 24 |
NINL1 | 37 | 38 | 141 | 224 | 150 | 112 | 38 | 150 | 187 | 75 | 75 | 136 | 37 |
NINL2 | 141 | 224 | 523 | 704 | 627 | 441 | 224 | 673 | 660 | 323 | 323 | 374 | 136 |
NINL3 | 523 | 704 | 1913 | 2931 | 2341 | 1823 | 704 | 2432 | 2397 | 1034 | 1034 | 1442 | 374 |
Networks | n | m | kmax | <k> | D | L | C | r |
---|---|---|---|---|---|---|---|---|
Contiguous | 49 | 107 | 8 | 4.367 | 11 | 4.163 | 0.497 | 0.2334 |
Dolphins | 62 | 159 | 12 | 5.129 | 8 | 3.357 | 0.259 | −0.0436 |
Polbooks | 105 | 441 | 25 | 8.4 | 7 | 3.079 | 0.488 | −0.1279 |
Word | 112 | 425 | 49 | 7.589 | 5 | 2.536 | 0.173 | −0.1293 |
Jazz | 198 | 2742 | 100 | 27.697 | 6 | 2.235 | 0.618 | 0.0202 |
Slavko | 324 | 2218 | 58 | 13.691 | 7 | 3.054 | 0.466 | 0.2473 |
USAir | 332 | 2126 | 139 | 12.807 | 6 | 2.738 | 0.625 | −0.2079 |
Netscience | 379 | 914 | 34 | 4.823 | 17 | 6.042 | 0.741 | −0.0817 |
Infectious | 410 | 2765 | 50 | 13.488 | 9 | 3.631 | 0.456 | 0.2258 |
1133 | 5451 | 71 | 9.622 | 8 | 3.606 | 0.220 | 0.0782 |
Networks | βth | β | τDC | τCC | τBC | τDNC | τCLD | τGM | τGLI | τNINL |
---|---|---|---|---|---|---|---|---|---|---|
Contiguous | 0.2027 | 0.20 | 0.7126 | 0.7253 | 0.5587 | 0.8155 | 0.8435 | 0.8690 | 0.8469 | 0.9099 |
Dolphin | 0.1470 | 0.15 | 0.7721 | 0.6187 | 0.5389 | 0.8355 | 0.7916 | 0.8731 | 0.8355 | 0.9344 |
Polbooks | 0.0838 | 0.09 | 0.7518 | 0.3679 | 0.3505 | 0.7679 | 0.8139 | 0.8198 | 0.5141 | 0.9229 |
Word | 0.0726 | 0.08 | 0.8311 | 0.8549 | 0.6523 | 0.8822 | 0.8388 | 0.9086 | 0.8784 | 0.9218 |
Jazz | 0.0259 | 0.03 | 0.8069 | 0.7080 | 0.4569 | 0.8175 | 0.8655 | 0.8505 | 0.8937 | 0.9322 |
Slavko | 0.0466 | 0.05 | 0.7719 | 0.7128 | 0.3625 | 0.8234 | 0.8538 | 0.8411 | 0.7938 | 0.9305 |
USAir | 0.0225 | 0.03 | 0.7251 | 0.8043 | 0.5081 | 0.8157 | 0.8854 | 0.8243 | 0.8522 | 0.9211 |
Netscience | 0.1247 | 0.13 | 0.5955 | 0.3292 | 0.3048 | 0.7724 | 0.7980 | 0.7788 | 0.6950 | 0.8395 |
Infectious | 0.0534 | 0.06 | 0.7281 | 0.6095 | 0.3707 | 0.7877 | 0.8105 | 0.8186 | 0.6984 | 0.9273 |
0.0535 | 0.06 | 0.7615 | 0.8138 | 0.6203 | 0.8330 | 0.8622 | 0.8226 | 0.8345 | 0.9255 |
Word Network | USAir Network | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Rank | DC | CC | BC | DNC | CLD | GM | GLI | NINL | Φ | Rank | DC | CC | BC | DNC | CLD | GM | GLI | NINL | Φ |
1 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 1 | 118 | 118 | 118 | 118 | 109 | 118 | 118 | 118 | 261 |
2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 261 | 261 | 8 | 261 | 131 | 261 | 261 | 261 | 118 |
3 | 44 | 52 | 44 | 52 | 52 | 52 | 52 | 52 | 52 | 3 | 255 | 67 | 261 | 255 | 112 | 255 | 255 | 255 | 255 |
4 | 52 | 44 | 52 | 44 | 44 | 44 | 44 | 44 | 44 | 4 | 152 | 255 | 201 | 182 | 299 | 182 | 182 | 182 | 182 |
5 | 105 | 28 | 10 | 105 | 51 | 105 | 105 | 105 | 105 | 5 | 182 | 201 | 47 | 152 | 118 | 152 | 152 | 152 | 230 |
6 | 10 | 105 | 80 | 10 | 105 | 10 | 25 | 51 | 10 | 6 | 230 | 182 | 182 | 230 | 255 | 230 | 230 | 230 | 176 |
7 | 25 | 10 | 105 | 28 | 22 | 25 | 51 | 10 | 25 | 7 | 166 | 47 | 255 | 166 | 176 | 166 | 67 | 112 | 152 |
8 | 28 | 27 | 28 | 25 | 55 | 51 | 28 | 26 | 51 | 8 | 67 | 166 | 152 | 67 | 147 | 67 | 166 | 166 | 147 |
9 | 51 | 25 | 2 | 51 | 25 | 28 | 26 | 25 | 28 | 9 | 112 | 248 | 313 | 112 | 261 | 112 | 112 | 67 | 67 |
10 | 2 | 26 | 29 | 26 | 32 | 26 | 10 | 55 | 55 | 10 | 201 | 112 | 13 | 201 | 301 | 147 | 147 | 147 | 166 |
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Zhu, J.; Wang, L. Identifying Influential Nodes in Complex Networks Based on Node Itself and Neighbor Layer Information. Symmetry 2021, 13, 1570. https://doi.org/10.3390/sym13091570
Zhu J, Wang L. Identifying Influential Nodes in Complex Networks Based on Node Itself and Neighbor Layer Information. Symmetry. 2021; 13(9):1570. https://doi.org/10.3390/sym13091570
Chicago/Turabian StyleZhu, Jingcheng, and Lunwen Wang. 2021. "Identifying Influential Nodes in Complex Networks Based on Node Itself and Neighbor Layer Information" Symmetry 13, no. 9: 1570. https://doi.org/10.3390/sym13091570
APA StyleZhu, J., & Wang, L. (2021). Identifying Influential Nodes in Complex Networks Based on Node Itself and Neighbor Layer Information. Symmetry, 13(9), 1570. https://doi.org/10.3390/sym13091570