Yıl 2019, Cilt 5 , Sayı 2, Sayfalar 73 - 76 2019-12-11

CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES
Ağ Kırılganlığı ve Laplasyen Enerjiler Arasındaki Korelasyonlar

Mehmet BALCI [1] , Ömer AKGÜLLER [2] , Erva KOL [3]


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.

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.

  • 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.
Birincil Dil en
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Orcid: 0000-0002-4650-8294
Yazar: Mehmet BALCI (Sorumlu Yazar)
Ülke: Turkey


Orcid: 0000-0002-7061-2534
Yazar: Ömer AKGÜLLER
Ülke: Turkey


Orcid: 0000-0002-1825-0097
Yazar: Erva KOL

Tarihler

Yayımlanma Tarihi : 11 Aralık 2019

Bibtex @araştırma makalesi { muglajsci610459, journal = {Mugla Journal of Science and Technology}, issn = {2149-3596}, address = {}, publisher = {Mugla Sitki Kocman University}, year = {2019}, volume = {5}, pages = {73 - 76}, doi = {10.22531/muglajsci.610459}, title = {CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES}, key = {cite}, author = {BALCI, Mehmet and AKGÜLLER, Ömer and KOL, Erva} }
APA BALCI, M , AKGÜLLER, Ö , KOL, E . (2019). CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology , 5 (2) , 73-76 . DOI: 10.22531/muglajsci.610459
MLA BALCI, M , AKGÜLLER, Ö , KOL, E . "CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES". Mugla Journal of Science and Technology 5 (2019 ): 73-76 <https://dergipark.org.tr/tr/pub/muglajsci/issue/49054/610459>
Chicago BALCI, M , AKGÜLLER, Ö , KOL, E . "CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES". Mugla Journal of Science and Technology 5 (2019 ): 73-76
RIS TY - JOUR T1 - CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES AU - Mehmet BALCI , Ömer AKGÜLLER , Erva KOL Y1 - 2019 PY - 2019 N1 - doi: 10.22531/muglajsci.610459 DO - 10.22531/muglajsci.610459 T2 - Mugla Journal of Science and Technology JF - Journal JO - JOR SP - 73 EP - 76 VL - 5 IS - 2 SN - 2149-3596- M3 - doi: 10.22531/muglajsci.610459 UR - https://doi.org/10.22531/muglajsci.610459 Y2 - 2019 ER -
EndNote %0 Mugla Journal of Science and Technology CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES %A Mehmet BALCI , Ömer AKGÜLLER , Erva KOL %T CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES %D 2019 %J Mugla Journal of Science and Technology %P 2149-3596- %V 5 %N 2 %R doi: 10.22531/muglajsci.610459 %U 10.22531/muglajsci.610459
ISNAD BALCI, Mehmet , AKGÜLLER, Ömer , KOL, Erva . "CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES". Mugla Journal of Science and Technology 5 / 2 (Aralık 2019): 73-76 . https://doi.org/10.22531/muglajsci.610459
AMA BALCI M , AKGÜLLER Ö , KOL E . CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology. 2019; 5(2): 73-76.
Vancouver BALCI M , AKGÜLLER Ö , KOL E . CORRELATIONS BETWEEN NETWORK VULNERABILITY AND LAPLACIAN ENERGIES. Mugla Journal of Science and Technology. 2019; 5(2): 76-73.