Research Article
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Ağ Kırılganlığı ve Laplasyen Enerjiler Arasındaki Korelasyonlar

Year 2019, Volume: 5 Issue: 2, 73 - 76, 11.12.2019
https://doi.org/10.22531/muglajsci.610459

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.

CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES

Year 2019, Volume: 5 Issue: 2, 73 - 76, 11.12.2019
https://doi.org/10.22531/muglajsci.610459

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.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Journals
Authors

Mehmet Balcı 0000-0002-4650-8294

Ömer Akgüller 0000-0002-7061-2534

Erva Kol This is me 0000-0002-1825-0097

Publication Date December 11, 2019
Published in Issue Year 2019 Volume: 5 Issue: 2

Cite

APA Balcı, M., Akgüller, Ö., & Kol, E. (2019). CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology, 5(2), 73-76. https://doi.org/10.22531/muglajsci.610459
AMA Balcı M, Akgüller Ö, Kol E. CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology. December 2019;5(2):73-76. doi:10.22531/muglajsci.610459
Chicago Balcı, Mehmet, Ömer Akgüller, and Erva Kol. “CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES”. Mugla Journal of Science and Technology 5, no. 2 (December 2019): 73-76. https://doi.org/10.22531/muglajsci.610459.
EndNote Balcı M, Akgüller Ö, Kol E (December 1, 2019) CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology 5 2 73–76.
IEEE M. Balcı, Ö. Akgüller, and E. Kol, “CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES”, Mugla Journal of Science and Technology, vol. 5, no. 2, pp. 73–76, 2019, doi: 10.22531/muglajsci.610459.
ISNAD Balcı, Mehmet et al. “CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES”. Mugla Journal of Science and Technology 5/2 (December 2019), 73-76. https://doi.org/10.22531/muglajsci.610459.
JAMA Balcı M, Akgüller Ö, Kol E. CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology. 2019;5:73–76.
MLA Balcı, Mehmet et al. “CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES”. Mugla Journal of Science and Technology, vol. 5, no. 2, 2019, pp. 73-76, doi:10.22531/muglajsci.610459.
Vancouver Balcı M, Akgüller Ö, Kol E. CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology. 2019;5(2):73-6.

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