Mathematical relation between extended connectivity and eigenvector coefficients.
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Mathematical relation between extended connectivity and eigenvector coefficients. / Rücker, Christoph; Rücker, Gerta.
In: Journal of Chemical Information and Computer Science, Vol. 34, No. 3, 01.05.1994, p. 534-538.Research output: Journal contributions › Journal articles › Research › peer-review
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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 Sciences
JF - Journal of Chemical Information and Computer Sciences
SN - 0095-2338
IS - 3
ER -