Abstract
Ağ analizinde kırılganlık kavramı önemli rol
oynamaktadır. Benzer şekilde, Laplasyen matrisleri de ağ analizinde etkili
araçlardır. Bu çalışmada, bu iki kavram arasındaki korelasyon incelenmiştir.
İlk olarak, oldukça çok bilinen ayrıt bağlantılık, tepe bağlantılık ve
yalnızlık sayıları hesaplanmıştır. Daha sonra, bu kırılganlık ölçüleri ile
Laplasyen matrislerinin enerjileri arasındaki korelasyon hesaplanmıştır. Sonuç
olarak, bir ağın Laplasyen enerjileri ile tepe bağlantılık ölçüsü arasında güçlü korelasyonlar bulunmuştur.
References
- Bagga, K.S., Beineke, W.D., Lipman, M.J. ve Pippert, R.E. (1994), Edge- Integrity : A Survey, Discrete Mathematics, 124: 3-12.
- Chvátal, V. (1973), Tough graphs and hamiltonian circuits, Discrete Math. 5:215-228.
- Cvetković, D., Rowlinson, P., Simić, S. (2007), Signless Laplacians of finite graphs, Lin. Algebra Appl., 423: 155–171.
- Boley, D., Ranjan, G., and Zhang, Z. (2011), Commute times for a directed graph using an asymmetric Laplacian, Lin. Alg. & Appl., 435: 224–242.
- Das, K.C. ve Mojallal, S.A. (2015), Relation between Energy and (Signless) Laplacian Energy of Graphs, MATCH Commun. Math. Comput. Chem., 74: 359-366.
- Diestel, R. (2005), Graph Theory, Springer Verlag Heidelberg, New York, 410s.
- Grone, R., Merris, R. ve Sunder, V.S. (1990), The Laplacian spectrum of a grap, SIAM J. Matrix Anal. Appl., 11: 218–238.
- Gutman, I. (1978), The energy of a graph, Ber. Math.-Statist. Sekt. Forschungsz. Graz 103: 1-22.
- Gutman, I. ve Zhou, B. (2006), Laplacian energy of a graph, Linear Algebra Appl. 414: 29–37.
- Güler, H. , Dündar, P. ve Balcı, M.A. (2011), Solitude Number at Graphs, I.J.Pure and Applied Mathematics, 66(3): 355-364.
- Lazić M. (2006), On the Laplacian Energy of a Graph, Czech. Math. Journal, 56 (131): 1207-1213.
- Pirzada, S., Ganie H.A. (2015), On the Consruction of L-Equienergetic Graphs, AKCE International Journal of Graphs and Combinatorics, 12:141-154.
Abstract
In the network analysis, vulnerability plays key
role. Similarly, Laplacian matrices are also effective tools in network
analysis. In this study, we examine correlations between those two concepts. We
first calculate the well-known vulnerability measures called edge connectivity,
vertex connectivity, and solitude number. Then, we find correlation between
vulnerability measures and energies of Laplacian matrices. As a result, we find
strong correlations between Laplacian energies and vertex connectivity of a
network.
References
- Bagga, K.S., Beineke, W.D., Lipman, M.J. ve Pippert, R.E. (1994), Edge- Integrity : A Survey, Discrete Mathematics, 124: 3-12.
- Chvátal, V. (1973), Tough graphs and hamiltonian circuits, Discrete Math. 5:215-228.
- Cvetković, D., Rowlinson, P., Simić, S. (2007), Signless Laplacians of finite graphs, Lin. Algebra Appl., 423: 155–171.
- Boley, D., Ranjan, G., and Zhang, Z. (2011), Commute times for a directed graph using an asymmetric Laplacian, Lin. Alg. & Appl., 435: 224–242.
- Das, K.C. ve Mojallal, S.A. (2015), Relation between Energy and (Signless) Laplacian Energy of Graphs, MATCH Commun. Math. Comput. Chem., 74: 359-366.
- Diestel, R. (2005), Graph Theory, Springer Verlag Heidelberg, New York, 410s.
- Grone, R., Merris, R. ve Sunder, V.S. (1990), The Laplacian spectrum of a grap, SIAM J. Matrix Anal. Appl., 11: 218–238.
- Gutman, I. (1978), The energy of a graph, Ber. Math.-Statist. Sekt. Forschungsz. Graz 103: 1-22.
- Gutman, I. ve Zhou, B. (2006), Laplacian energy of a graph, Linear Algebra Appl. 414: 29–37.
- Güler, H. , Dündar, P. ve Balcı, M.A. (2011), Solitude Number at Graphs, I.J.Pure and Applied Mathematics, 66(3): 355-364.
- Lazić M. (2006), On the Laplacian Energy of a Graph, Czech. Math. Journal, 56 (131): 1207-1213.
- Pirzada, S., Ganie H.A. (2015), On the Consruction of L-Equienergetic Graphs, AKCE International Journal of Graphs and Combinatorics, 12:141-154.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Journals |
| Authors | |
| Publication Date | December 11, 2019 |
| Published in Issue | Year 2019 |
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