Integrating Node Importance and Network Topological Properties for Link Prediction in Complex Network
<p>The framework of DCCLP algorithm.</p> "> Figure 2
<p>The indicator AUC and Precision of ten algorithms on a set of real-world networks. For almost all networks (expect <span class="html-italic">C. elegans</span> and NetScience), the DCCLP algorithm surpasses all comparison algorithms.</p> "> Figure 3
<p>The indicator AUC and Precision of the DCCLP algorithm and the comparative link prediction algorithms.</p> ">
Abstract
:1. Introduction
2. The TPSR3 Algorithm
3. The DCCLP Algorithm
4. The Parameter Estimation of DCCLP Algorithm
5. Experimental Results and Analysis
- (1)
- Comparison of prediction accuracy between DCCLP algorithm and algorithms in [17]
- (2)
- Comparison of the DCCLP algorithm with existing algorithms
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Rossetti, G.; Cazabet, R. Community discovery in dynamic networks: A survey. ACM Comput. Surv. 2018, 51, 1–37. [Google Scholar] [CrossRef] [Green Version]
- Shakibian, H.; Moghadam Charkari, N. Mutual information model for link prediction in heterogeneous complex networks. Sci. Rep. 2017, 7, 44981. [Google Scholar] [CrossRef]
- Zareie, A.; Sheikhahmadi, A.; Jalili, M. Influential node ranking in social networks Based on neighborhood diversity. Future Gener. Comput. Syst. 2019, 94, 120–129. [Google Scholar] [CrossRef]
- Zhang, F.; Liu, J.; Zuo, C. Research of complex network dynamics evolution. In Information Engineering and Applications; Springer: London, UK, 2012; pp. 806–815. [Google Scholar]
- Lü, L. Link Prediction on Complex networks. J. Univ. Electron. Sci. Technol. China 2010, 39, 651–661. [Google Scholar]
- Clauset, A.; Moore, C.; Newman, M.E.J. Hierarchical structure and the prediction of Missing links in networks. Nature 2008, 453, 98–101. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Zhang, D.; Yin, J.; Zhu, X.; Zhang, C. Network representation learning: A survey. IEEE Trans. Big Data 2018, 6, 3–28. [Google Scholar] [CrossRef] [Green Version]
- Rapoport, A. Spread of information through a population with socio-structural bias: I. Assumption of transitivity. Bull. Math. Biol. 1953, 15, 523–533. [Google Scholar] [CrossRef]
- Adamic, L.A.; Adar, E. Friends and neighbors on the Web. Soc. Netw. 2003, 25, 211–230. [Google Scholar] [CrossRef] [Green Version]
- Zhou, T.; Lü, L.; Zhang, Y.C. Predicting missing links via local information. Eur. Phys. J. B 2009, 71, 623–630. [Google Scholar] [CrossRef] [Green Version]
- Gao, Y.; Zhang, Y.P.; Qian, F.L.; Zhao, S. Combined with Node Degree and Node Clustering of Link Prediction Algorithm. J. Chin. Comput. Syst. 2017, 38, 1436–1441. [Google Scholar]
- Yu, Y.; Wang, Y.G.; Luo, Z.G.; Yang, Y.; Wang, X.; Gao, T.; Yu, Q. Link Prediction algorithm based on clustering coefficient and node centrality. J. Tsinghua Univ. (Sci. Technol.) 2022, 62, 98–104. [Google Scholar]
- Katz, L. A new status index derived from sociometric analysis. Psychometrika 1953, 18, 39–43. [Google Scholar] [CrossRef]
- Brin, S.; Page, L. The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 1998, 30, 107–117. [Google Scholar] [CrossRef]
- Lv, L.Y.; Jin, C.H.; Zhou, T. Similarity index based on local paths for link prediction of Complex networks. Phys. Rev. E 2009, 80, 046122. [Google Scholar]
- Liu, W.; Lv, L.Y. Link prediction based on local random walk. Europhys. Lett. 2010, 89, 58007. [Google Scholar] [CrossRef] [Green Version]
- Qian, F.; Gao, Y.; Zhao, S.; Tang, J.; Zhang, Y. Combining topological properties and strong ties for Link prediction. Tsinghua Sci. Technol. 2017, 22, 595–608. [Google Scholar] [CrossRef]
- Wu, Z.; Lin, Y.; Wang, J.; Gregory, S. Link prediction with node clustering coefficient. Phys. A Stat. Mech. Its Appl. 2016, 452, 1–8. [Google Scholar] [CrossRef] [Green Version]
- Mumin, D.; Shi, L.L.; Liu, L. An efficient algorithm for link prediction based on local Information: Considering the effect of node degree. Concurr. Comput. Pract. Exp. 2022, 34, 6289. [Google Scholar] [CrossRef]
- Liu, Y.; Liu, S.; Yu, F.; Yang, X. Link prediction algorithm based on the initial information Contribution of nodes. Inf. Sci. 2022, 608, 1591–1616. [Google Scholar] [CrossRef]
- Fu, X.Y.; Gu, Y.J. Unsupervised Link Prediction Algorithm Fusing Node Importance. Comput. Eng. Appl. 2022, 58, 94–101. [Google Scholar]
- Liu, B.; Xu, S.; Li, T.; Xiao, J.; Xu, X.K. Quantifying the effects of topology and weight for link prediction in weighted complex networks. Entropy 2018, 20, 363. [Google Scholar] [CrossRef] [PubMed]
- Samei, Z.; Jalili, M. Application of hyperbolic geometry in link prediction of multiplex networks. Sci. Rep. 2019, 9, 12604. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Braik, M.; Hammouri, A.; Atwan, J.; Al-Betar, M.A.; Awadallah, M.A. White Shark Optimizer: A novel bio-inspired metaheuristic algorithm for global optimization problems. Knowl.-Based Syst. 2022, 243, 108457. [Google Scholar] [CrossRef]
Networks | CCN | TPSR2 | TPSR3 | TPSR4 | CN | AA | RA | LP (0.01) | Katz (0.01) | DCCLP θ*, α* |
---|---|---|---|---|---|---|---|---|---|---|
Jazz | 0.9710 | 0.9710 | 0.9220 | 0.9130 | 0.9550 | 0.9620 | 0.9710 | 0.9470 | 0.9420 | 0.9720 (0.0001, 1) |
USAir | 0.9530 | 0.9540 | 0.9260 | 0.9200 | 0.9370 | 0.9480 | 0.9530 | 0.9270 | 0.9240 | 0.9703 (0.0013, 0.9798) |
C. elegans | 0.8980 | 0.8640 | 0.8710 | 0.8630 | 0.8430 | 0.8600 | 0.8630 | 0.8590 | 0.8560 | 0.8602 (0.0422, 0.9242) |
FWFW | 0.7580 | 0.6250 | 0.8080 | 0.7860 | 0.6110 | 0.6130 | 0.6160 | 0.6720 | 0.6790 | 0.8143 (0.0943, 0.0290) |
FWFD | 0.7570 | 0.6200 | 0.8080 | 0.7860 | 0.6100 | 0.6100 | 0.6130 | 0.6720 | 0.6800 | 0.8168 (0.0819, 0.0478) |
FWEW | 0.8120 | 0.7130 | 0.8410 | 0.8320 | 0.6920 | 0.6990 | 0.7070 | 0.7360 | 0.7410 | 0.8505 (0.0713, 0.0042) |
FWMW | 0.7930 | 0.7140 | 0.8180 | 0.8040 | 0.7020 | 0.7070 | 0.7110 | 0.7390 | 0.7400 | 0.8249 (0.0829, 0.0571) |
PB | 0.9420 | 0.9230 | 0.9320 | 0.9270 | 0.9190 | 0.9210 | 0.9230 | 0.9300 | 0.9240 | 0.9430 (0.0366, 0.7578) |
Netscience | 0.9400 | 0.9350 | 0.9400 | 0.9400 | 0.9360 | 0.9360 | 0.9350 | 0.9400 | 0.9400 | 0.9989 (0.0822, 0.0160) |
Networks | CCN | TPSR2 | TPSR3 | TPSR4 | CN | AA | RA | LP (0.01) | Katz (0.01) | DCCLP θ*, α* |
---|---|---|---|---|---|---|---|---|---|---|
Jazz | 0.8240 | 0.8380 | 0.6500 | 0.6000 | 0.8190 | 0.8380 | 0.8240 | 0.7840 | 0.8090 | 0.8390 (0.0001, 1) |
USAir | 0.6270 | 0.6310 | 0.5710 | 0.5610 | 0.5910 | 0.6070 | 0.6270 | 0.5860 | 0.5900 | 0.6374 (0.0013, 0.9798) |
C. elegans | 0.1430 | 0.1330 | 0.1590 | 0.1520 | 0.1320 | 0.1340 | 0.1330 | 0.1360 | 0.1360 | 0.1587 (0.0422, 0.9242) |
FWFW | 0.1600 | 0.0880 | 0.3420 | 0.2900 | 0.0900 | 0.0900 | 0.0860 | 0.1300 | 0.0980 | 0.3868 (0.0943, 0.0290) |
FWFD | 0.1680 | 0.0910 | 0.3510 | 0.2990 | 0.0900 | 0.0890 | 0.0870 | 0.1310 | 0.0950 | 0.3955 (0.0819, 0.0478) |
FWEW | 0.2600 | 0.1700 | 0.3200 | 0.3060 | 0.1470 | 0.1570 | 0.1650 | 0.1850 | 0.1580 | 0.3768 (0.0713, 0.0042) |
FWMW | 0.2270 | 0.1470 | 0.3340 | 0.3010 | 0.1390 | 0.1440 | 0.1450 | 0.1740 | 0.1470 | 0.3818 (0.0829, 0.0571) |
PB | 0.2980 | 0.2470 | 0.5030 | 0.4830 | 0.4050 | 0.3610 | 0.2400 | 0.4430 | 0.4130 | 0.5075 (0.0366, 0.7578) |
Netscience | 0.9700 | 0.9720 | 0.9710 | 0.9710 | 0.8160 | 0.9660 | 0.9640 | 0.8100 | 0.8100 | 0.8409 (0.0822, 0.0160) |
Networks | D | H | |||||
---|---|---|---|---|---|---|---|
Polbook | 105 | 441 | 8.400 | 0.4875 | 0.0808 | 1.4207 | 3.0788 |
Dolphin | 62 | 159 | 5.129 | 0.3852 | 0.0841 | 1.3243 | 3.1089 |
karate | 34 | 78 | 4.5882 | 0.6001 | 0.1390 | 1.6933 | 2.4082 |
FWEW | 69 | 880 | 25.5072 | 0.5521 | 0.3751 | 1.2746 | 1.636 |
FWFW | 128 | 2075 | 32.4219 | 0.3346 | 0.2553 | 1.2370 | 1.7763 |
FWMW | 97 | 1446 | 29.8144 | 0.4683 | 0.3106 | 1.2656 | 1.6929 |
football | 115 | 613 | 10.6609 | 0.4032 | 0.0935 | 1.0069 | 2.5082 |
Grassland | 75 | 114 | 3.0400 | 0.8198 | 0.0411 | 2.7499 | 3.1996 |
Trainbombing | 64 | 243 | 7.5938 | 0.7473 | 0.1205 | 1.6588 | 2.691 |
C. elegans | 297 | 2148 | 14.4646 | 0.3429 | 0.0489 | 1.8008 | 2.4553 |
USAir | 332 | 2126 | 12.8072 | 0.7909 | 0.0387 | 3.4639 | 2.7381 |
Infectious | 410 | 2765 | 13.4878 | 0.4802 | 0.0330 | 1.3876 | 3.6309 |
FWFD | 128 | 2106 | 32.9063 | 0.3346 | 0.2591 | 1.2307 | 1.7724 |
Metabolic | 453 | 2025 | 8.9404 | 0.6597 | 0.0198 | 4.485 | 2.6638 |
Jazz | 198 | 2742 | 27.6970 | 0.6427 | 0.1406 | 1.3951 | 2.235 |
US Roads | 49 | 107 | 4.3673 | 0.5171 | 0.0910 | 1.1299 | 4.1633 |
PB | 1222 | 16,714 | 27.3552 | 0.4307 | 0.0224 | 2.9707 | 2.7375 |
Netscience | 1589 | 2742 | 3.4512 | 0.8310 | 0.0022 | 2.0105 | 0.3514 |
1133 | 5451 | 9.6222 | 0.3535 | 0.0085 | 1.9421 | 3.606 | |
Bio-DM-LC | 658 | 1129 | 3.4316 | 0.5166 | 0.0052 | 3.1149 | 3.5637 |
Bio-CE-GT | 924 | 3239 | 7.0108 | 0.6820 | 0.0076 | 4.1392 | 3.3724 |
Networks | CN2D | CCLP | CCNC | DCCLP θ*, α* |
---|---|---|---|---|
Polbook | 0.8791 | 0.8908 | 0.9240 [12] | 0.8876 (0.0826, 0.7284) |
Dolphin | 0.7722 | 0.8020 [18] | 0.8360 [12] | 0.7981 (0.0883, 0.0735) |
karate | 0.6441 | 0.6960 | 0.7332 | 0.7925 (0.0960, 0.0784) |
FWEW | 0.6750 | 0.7026 | 0.7216 | 0.8505 (0.0713, 0.0042) |
FWFW | 0.6042 | 0.6362 [18] | 0.6470 [12] | 0.8143 (0.0943, 0.290) |
FWMW | 0.7079 | 0.7229 | 0.7267 | 0.8249 (0.0829, 0.0571) |
football | 0.8535 | 0.8397 | 0.8420 | 0.8472 (0.0834, 0.002) |
Grassland | 0.8236 | 0.7900 [18] | 0.8987 | 0.8655 (0.0891, 0.0606) |
Trainbombing | 0.9283 | 0.9317 | 0.9424 | 0.9328 (0.0296, 0.9077) |
C. elegans | 0.8613 [19] | 0.8658 | 0.8721 | 0.8602 (0.0422, 0.9242) |
USAir | 0.9695 [19] | 0.9576 | 0.9620 [12] | 0.9703 (0.0013, 0.9798) |
Infectious | 0.9393 | 0.9399 | 0.9447 | 0.9579 (0.0156, 0.6831) |
FWFD | 0.6003 | 0.6308 | 0.6318 | 0.8168 (0.0819, 0.0478) |
metabolic | 0.9039 | 0.9507 | 0.9592 | 0.9542 (0.0034, 1.0000) |
Jazz | 0.9685 [19] | 0.9600 [18] | 0.9740 [12] | 0.9716 (0.0001, 1.000) |
USRoads | 0.9007 | 0.8647 | 0.8829 | 0.8182 (0.0892, 0.0566) |
0.8546 | 0.8570 [18] | 0.8578 | 0.9168 (0.0504, 0.5232) | |
bio-DM-LC | 0.6701 | 0.6498 | 0.6707 | 0.9684 (0.0411, 0.0007) |
bio-CE-GT | 0.9341 | 0.9403 | 0.9547 | 0.9717 (0.0168, 0.7671) |
PB | 0.9599 [19] | 0.9266 [18] | 0.9360 [12] | 0.9397 (0.0366, 0.7578) |
Netscience | 0.9981 [19] | 0.9480 | 0.9920 | 0.9989 (0.0822, 0.0160) |
Networks | CN2D | CCLP | CCNC | DCCLP θ*, α* |
---|---|---|---|---|
Polbook | 0.1145 | 0.1426 | 0.1485 | 0.1257 (0.0826, 0.7284) |
Dolphin | 0.0646 | 0.0528 | 0.0576 | 0.0551 (0.0883, 0.0735) |
karate | 0.0307 | 0.0385 | 0.0424 | 0.0489 (0.0960, 0.0784) |
FWEW | 0.1423 | 0.1671 | 0.1978 | 0.3768 (0.0713, 0.0042) |
FWFW | 0.0853 | 0.0970 [18] | 0.1068 | 0.3868 (0.0943, 0.290) |
FWMW | 0.1320 | 0.1440 | 0.1735 | 0.3818 (0.0829, 0.0571) |
football | 0.3112 | 0.2619 | 0.2738 | 0.2477 (0.0834, 0.002) |
Grassland | 0.0441 | 0.0565 | 0.0698 | 0.0465 (0.0891, 0.0606) |
Trainbombing | 0.1791 | 0.1912 | 0.2083 | 0.1777 (0.0296, 0.9077) |
C. elegans | 0.1213 | 0.1356 | 0.1316 | 0.1587 (0.0422, 0.9242) |
USAir | 0.6046 | 0.6166 | 0.6503 | 0.6374 (0.0013, 0.9798) |
Infectious | 0.3803 | 0.3592 | 0.5083 | 0.2720 (0.0156, 0.6831) |
FWFD | 0.0862 | 0.0967 | 0.1109 | 0.3955 (0.0819, 0.0478) |
metabolic | 0.1918 | 0.2467 | 0.3188 | 0.2929 (0.0034, 1.0000) |
Jazz | 0.8243 | 0.8590 [18] | 0.8297 | 0.8385 (0.0001, 1.000) |
USRoads | 0.0800 | 0.0603 | 0.0657 | 0.0238 (0.0892, 0.0566) |
0.2953 | 0.3080 [18] | 0.2878 | 0.1850 (0.0504, 0.5232) | |
bio-DM-LC | 0.0043 | 0.0456 | 0.0207 | 0.4751 (0.0411, 0.0007) |
bio-CE-GT | 0.1076 | 0.1911 | 0.2228 | 0.2961 (0.0168, 0.7671) |
PB | 0.4288 | 0.4040 [18] | 0.2732 | 0.5075 (0.0366, 0.7578) |
Netscience | 0.8464 | 0.8982 | 0.6241 | 0.8409 (0.0822, 0.0160) |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhu, J.; Dai, F.; Zhao, F.; Guo, W. Integrating Node Importance and Network Topological Properties for Link Prediction in Complex Network. Symmetry 2023, 15, 1492. https://doi.org/10.3390/sym15081492
Zhu J, Dai F, Zhao F, Guo W. Integrating Node Importance and Network Topological Properties for Link Prediction in Complex Network. Symmetry. 2023; 15(8):1492. https://doi.org/10.3390/sym15081492
Chicago/Turabian StyleZhu, Junxi, Fang Dai, Fengqun Zhao, and Wenyan Guo. 2023. "Integrating Node Importance and Network Topological Properties for Link Prediction in Complex Network" Symmetry 15, no. 8: 1492. https://doi.org/10.3390/sym15081492
APA StyleZhu, J., Dai, F., Zhao, F., & Guo, W. (2023). Integrating Node Importance and Network Topological Properties for Link Prediction in Complex Network. Symmetry, 15(8), 1492. https://doi.org/10.3390/sym15081492