TY - JOUR

T1 - Mathematical relation between extended connectivity and eigenvector coefficients.

AU - Rücker, Christoph

AU - Rücker, Gerta

N1 - Print Edition ISSN: 1549-9596. Web Edition ISSN: 1549-960X Druckausg. 45.2004 -: Journal of chemical information and modeling

PY - 1994/5/1

Y1 - 1994/5/1

N2 - Formulas are derived for the limit distribution of weights of vertices in a graph as obtained from extended connectivities. A fundamental difference between bipartite and nonbipartite graphs is seen: For the latter the eventual distribution coincides with the one resulting from the coefficients in the principal eigenvector. For the former, in contrast, the last eigenvector also has to be taken into account, and there is no single limit distribution. This is the reason why in some bipartite graphs the ranks derived from extended connectivities switch indefinitely for certain atoms.

AB - Formulas are derived for the limit distribution of weights of vertices in a graph as obtained from extended connectivities. A fundamental difference between bipartite and nonbipartite graphs is seen: For the latter the eventual distribution coincides with the one resulting from the coefficients in the principal eigenvector. For the former, in contrast, the last eigenvector also has to be taken into account, and there is no single limit distribution. This is the reason why in some bipartite graphs the ranks derived from extended connectivities switch indefinitely for certain atoms.

KW - Chemistry

UR - http://www.scopus.com/inward/record.url?scp=0028428113&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0bef4650-a816-3582-8d5b-9404d998cb6f/

U2 - 10.1021/ci00019a010

DO - 10.1021/ci00019a010

M3 - Journal articles

VL - 34

SP - 534

EP - 538

JO - Journal of Chemical Information and Computer Science

JF - Journal of Chemical Information and Computer Science

SN - 0095-2338

IS - 3

ER -