84:
mathematically manipulated so as to derive a single number, usually known as graph invariant, graph-theoretical index or topological index. As a result, the topological index can be defined as two-dimensional descriptors that can be easily calculated from the molecular graphs, and do not depend on the way the graph is depicted or labeled and no need of energy minimization of the chemical structure.
83:
Topological descriptors are derived from hydrogen-suppressed molecular graphs, in which the atoms are represented by vertices and the bonds by edges. The connections between the atoms can be described by various types of topological matrices (e.g., distance or adjacency matrices), which can be
166:
is another important characteristic of topological index. The Wiener index, Randic's molecular connectivity index, Balaban's J index may be calculated by fast algorithms, in contrast to Hosoya index and its modifications for which non-exponential algorithms are unknown.
897:
Roy K, Ghosh G (November 2007). "QSTR with extended topochemical atom (ETA) indices. 9. Comparative QSAR for the toxicity of diverse functional organic compounds to
Chlorella vulgaris using chemometric tools".
788:
Roy K, Ghosh G (February 2005). "QSTR with extended topochemical atom indices. Part 5: Modeling of the acute toxicity of phenylsulfonyl carboxylates to Vibrio fischeri using genetic function approximation".
92:
The simplest topological indices do not recognize double bonds and atom types (C, N, O etc.) and ignore hydrogen atoms ("hydrogen suppressed") and defined for connected undirected
461:
Chemical applications of topology and graph theory: a collection of papers from a symposium held at the
University of Georgia, Athens, Georgia, U. S. A., 18–22 April 1983
559:
Pal DK, Sengupta C, De AU (1989). "Introduction of A Novel
Topochemical Index and Exploitation of Group Connectivity Concept to Achieve Predictability in QSAR and RDD".
853:
Roy K, Sanyal I, Roy PP (December 2006). "QSPR of the bioconcentration factors of non-ionic organic compounds in fish using extended topochemical atom (ETA) indices".
147:
A topological index may have the same value for a subset of different molecular graphs, i.e. the index is unable to discriminate the graphs from this subset. The
268:(including desirable therapeutic effect and undesirable side effects) of chemicals (drugs/toxicants/environmental pollutants) with descriptors representative of
817:
Roy K, Ghosh G (February 2006). "QSTR with extended topochemical atom (ETA) indices. VI. Acute toxicity of benzene derivatives to tadpoles (Rana japonica)".
361:
64:
109:
104:
is the first topological index recognized in chemical graph theory, and it is often referred to as "the" topological index. Other examples include the
151:
is very important characteristic of topological index. To increase the discrimination capability a few topological indices may be combined to
540:
Pal DK, Sengupta C, De AU (1988). "A new topochemical descriptor (TAU) in molecular connectivity concept: Part I--Aliphatic compounds".
116:, and the TAU descriptors. The extended topochemical atom (ETA) indices have been developed based on refinement of TAU descriptors.
955:
486:"Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons"
468:
413:
González-DĂaz H, González-DĂaz Y, Santana L, Ubeira FM, Uriarte E (February 2008). "Proteomics, networks and connectivity indices".
344:
317:
17:
996:
163:
991:
675:
399:
52:
236:
1001:
760:
Roy K, Ghosh G (2004). "QSTR with extended topochemical atom indices. 2. Fish toxicity of substituted benzenes".
1006:
241:
211:
362:"Medicinal chemistry and bioinformatics--current trends in drugs discovery with networks topological indices"
32:
639:
Bonchev D, Mekenyan O, Trinajstić N (1981). "Isomer discrimination by topological information approach".
393:
97:
24:
113:
231:
907:
862:
718:
44:
28:
580:"Extended Topochemical Atom (ETA) Indices in the Valence Electron Mobile (VEM) Environment as Tools"
291:
For example, ETA indices have been applied in the development of predictive QSAR/QSPR/QSTR models.
226:
265:
139:
for every atom in a molecule. Another examples of local indices are modifications of Hosoya index.
221:
216:
886:
842:
742:
656:
621:
438:
308:
Hendrik
Timmerman; Todeschini, Roberto; Viviana Consonni; Raimund Mannhold; Hugo Kubinyi (2002).
273:
269:
186:
72:
951:
923:
878:
834:
806:
777:
734:
604:
Trofimov MI (1991). "An optimization of the procedure for the calculation of Hosoya's index".
464:
430:
381:
340:
313:
261:
201:
915:
870:
826:
798:
769:
726:
687:
648:
613:
497:
422:
373:
285:
277:
93:
60:
48:
196:
911:
866:
722:
519:
281:
919:
985:
660:
625:
334:
191:
890:
846:
746:
695:
442:
206:
181:
176:
128:
124:
105:
101:
68:
377:
874:
830:
802:
730:
67:(QSARs) in which the biological activity or other properties of molecules are
691:
51:
of a chemical compound. Topological indices are numerical parameters of a
927:
882:
838:
810:
781:
738:
434:
426:
385:
652:
579:
502:
485:
56:
96:
only. More sophisticated topological indices also take into account the
617:
773:
973:
63:. Topological indices are used for example in the development of
257:
280:, toxicity prediction, and regulatory decisions in addition to
674:
Tong W, Hong H, Xie Q, Shi L, Fang H, Perkins R (April 2005).
948:
Topological
Indices and Related Descriptors in QSAR and QSPAR
135:
to describe entire molecule, Bonchev and
Polansky introduced
709:
Dearden JC (2003). "In silico prediction of drug toxicity".
276:. QSARs are being applied in many disciplines for example
264:
derived from application of statistical tools correlating
676:"Assessing QSAR Limitations – A Regulatory Perspective"
360:
González-DĂaz H, Vilar S, Santana L, Uriarte E (2007).
972:
Software for calculating various topological indices:
762:
Journal of
Chemical Information and Computer Sciences
336:
Molecular connectivity in chemistry and drug research
100:
of each of the atoms contained in the molecule. The
946:Balaban, Alexandru T.; James Devillers (2000).
584:Internet Electronic Journal of Molecular Design
388:. Archived from the original on April 14, 2013.
518:Katritzky AR, Karelson M, Petrukhin R (2002).
65:quantitative structure-activity relationships
8:
16:For topological indices in mathematics, see
711:Journal of Computer-aided Molecular Design
143:Discrimination capability and superindices
501:
490:Bulletin of the Chemical Society of Japan
333:Hall, Lowell H.; Kier, Lemont B. (1976).
300:
855:SAR and QSAR in Environmental Research
599:
597:
454:
452:
391:
366:Current Topics in Medicinal Chemistry
110:Randić's molecular connectivity index
7:
791:Bioorganic & Medicinal Chemistry
680:Current Computer-Aided Drug Design
641:Journal of Computational Chemistry
14:
920:10.1016/j.chemosphere.2007.07.037
606:Journal of Mathematical Chemistry
310:Handbook of Molecular Descriptors
47:that is calculated based on the
1:
819:Journal of Molecular Modeling
237:Atom bond connectivity index
171:List of topological indices
18:Atiyah–Singer index theorem
1023:
378:10.2174/156802607780906771
339:. Boston: Academic Press.
137:local (differential) index
15:
875:10.1080/10629360601033499
831:10.1007/s00894-005-0033-7
803:10.1016/j.bmc.2004.11.014
520:"Topological Descriptors"
398:: CS1 maint: unfit URL (
149:discrimination capability
133:global (integral) indices
692:10.2174/1573409053585663
242:Merrifield-Simmons index
164:Computational complexity
159:Computational complexity
120:Global and local indices
731:10.1023/A:1025361621494
578:Roy K, Ghosh G (2003).
522:. University of Florida
463:. Amsterdam: Elsevier.
459:King, R. Bruce (1983).
312:. Weinheim: Wiley-VCH.
55:which characterize its
997:Mathematical chemistry
484:Hosoya, Haruo (1971).
427:10.1002/pmic.200700638
33:mathematical chemistry
992:Theoretical chemistry
653:10.1002/jcc.540020202
260:represent predictive
25:chemical graph theory
503:10.1246/bcsj.44.2332
45:molecular descriptor
950:. Boca Raton: CRC.
912:2007Chmsp..70....1R
867:2006SQER...17..563R
723:2003JCAMD..17..119D
270:molecular structure
266:biological activity
212:Padmakar–Ivan index
98:hybridization state
618:10.1007/BF01166946
187:Hyper-Wiener index
73:chemical structure
41:connectivity index
39:, also known as a
29:molecular topology
774:10.1021/ci0342066
286:lead optimization
114:Balaban’s J index
43:, is a type of a
37:topological index
23:In the fields of
1014:
1002:Graph invariants
961:
932:
931:
894:
850:
814:
785:
757:
751:
750:
706:
700:
699:
694:. Archived from
671:
665:
664:
636:
630:
629:
601:
592:
591:
575:
569:
568:
556:
550:
549:
537:
531:
530:
528:
527:
515:
509:
507:
505:
496:(9): 2332–2339.
481:
475:
474:
456:
447:
446:
410:
404:
403:
397:
389:
357:
351:
350:
330:
324:
323:
305:
232:Arithmetic index
94:molecular graphs
59:and are usually
1022:
1021:
1017:
1016:
1015:
1013:
1012:
1011:
1007:Cheminformatics
982:
981:
969:
964:
958:
945:
941:
939:Further reading
936:
935:
896:
852:
816:
787:
759:
758:
754:
717:(2–4): 119–27.
708:
707:
703:
673:
672:
668:
638:
637:
633:
603:
602:
595:
577:
576:
572:
558:
557:
553:
539:
538:
534:
525:
523:
517:
516:
512:
483:
482:
478:
471:
458:
457:
450:
412:
411:
407:
390:
372:(10): 1015–29.
359:
358:
354:
347:
332:
331:
327:
320:
307:
306:
302:
297:
278:risk assessment
255:
250:
173:
161:
145:
122:
90:
81:
61:graph invariant
49:molecular graph
21:
12:
11:
5:
1020:
1018:
1010:
1009:
1004:
999:
994:
984:
983:
980:
979:
968:
967:External links
965:
963:
962:
956:
942:
940:
937:
934:
933:
797:(4): 1185–94.
752:
701:
698:on 2010-06-20.
686:(2): 195–205.
666:
647:(2): 127–148.
631:
612:(1): 327–332.
593:
570:
561:Indian J. Chem
551:
542:Indian J. Chem
532:
510:
476:
469:
448:
405:
352:
345:
325:
318:
299:
298:
296:
293:
282:drug discovery
254:
251:
249:
246:
245:
244:
239:
234:
229:
227:Harmonic index
224:
219:
214:
209:
204:
199:
194:
189:
184:
179:
172:
169:
160:
157:
144:
141:
121:
118:
89:
86:
80:
77:
13:
10:
9:
6:
4:
3:
2:
1019:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
989:
987:
977:
976:
971:
970:
966:
959:
957:90-5699-239-2
953:
949:
944:
943:
938:
929:
925:
921:
917:
913:
909:
905:
901:
892:
888:
884:
880:
876:
872:
868:
864:
861:(6): 563–82.
860:
856:
848:
844:
840:
836:
832:
828:
825:(3): 306–16.
824:
820:
812:
808:
804:
800:
796:
792:
783:
779:
775:
771:
768:(2): 559–67.
767:
763:
756:
753:
748:
744:
740:
736:
732:
728:
724:
720:
716:
712:
705:
702:
697:
693:
689:
685:
681:
677:
670:
667:
662:
658:
654:
650:
646:
642:
635:
632:
627:
623:
619:
615:
611:
607:
600:
598:
594:
589:
585:
581:
574:
571:
566:
562:
555:
552:
547:
543:
536:
533:
521:
514:
511:
504:
499:
495:
491:
487:
480:
477:
472:
470:0-444-42244-7
466:
462:
455:
453:
449:
444:
440:
436:
432:
428:
424:
421:(4): 750–78.
420:
416:
409:
406:
401:
395:
387:
383:
379:
375:
371:
367:
363:
356:
353:
348:
346:0-12-406560-0
342:
338:
337:
329:
326:
321:
319:3-527-29913-0
315:
311:
304:
301:
294:
292:
289:
287:
283:
279:
275:
271:
267:
263:
259:
252:
247:
243:
240:
238:
235:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
208:
205:
203:
202:Zagreb indics
200:
198:
195:
193:
192:Estrada index
190:
188:
185:
183:
180:
178:
175:
174:
170:
168:
165:
158:
156:
154:
150:
142:
140:
138:
134:
130:
126:
119:
117:
115:
111:
107:
103:
99:
95:
87:
85:
78:
76:
74:
70:
66:
62:
58:
54:
50:
46:
42:
38:
34:
30:
26:
19:
974:
947:
903:
899:
858:
854:
822:
818:
794:
790:
765:
761:
755:
714:
710:
704:
696:the original
683:
679:
669:
644:
640:
634:
609:
605:
587:
583:
573:
564:
560:
554:
545:
541:
535:
524:. Retrieved
513:
493:
489:
479:
460:
418:
414:
408:
394:cite journal
369:
365:
355:
335:
328:
309:
303:
290:
256:
222:sombor index
217:Gutman index
207:Szeged index
197:Randić index
182:Hosoya index
177:Wiener index
162:
152:
148:
146:
136:
132:
129:Wiener index
125:Hosoya index
123:
106:Wiener index
102:Hosoya index
91:
82:
40:
36:
22:
906:(1): 1–12.
900:Chemosphere
248:Application
79:Calculation
71:with their
986:Categories
590:: 599–620.
567:: 261–267.
548:: 734–739.
526:2009-05-06
415:Proteomics
295:References
274:properties
153:superindex
69:correlated
661:120705298
626:121743373
975:GraphTea
928:17765287
891:10707472
883:17162387
847:30293729
839:16249936
811:15670927
782:15032536
747:21518449
739:13677480
443:20599466
435:18297652
386:17508935
57:topology
908:Bibcode
863:Bibcode
719:Bibcode
272:and/or
954:
926:
889:
881:
845:
837:
809:
780:
745:
737:
659:
624:
467:
441:
433:
384:
343:
316:
262:models
31:, and
887:S2CID
843:S2CID
743:S2CID
657:S2CID
622:S2CID
439:S2CID
258:QSARs
88:Types
53:graph
952:ISBN
924:PMID
879:PMID
835:PMID
807:PMID
778:PMID
735:PMID
465:ISBN
431:PMID
400:link
382:PMID
341:ISBN
314:ISBN
284:and
253:QSAR
131:are
127:and
35:, a
916:doi
871:doi
827:doi
799:doi
770:doi
727:doi
688:doi
649:doi
614:doi
565:28B
546:27B
498:doi
423:doi
374:doi
988::
922:.
914:.
904:70
902:.
895:;
885:.
877:.
869:.
859:17
857:.
851:;
841:.
833:.
823:12
821:.
815:;
805:.
795:13
793:.
786:;
776:.
766:44
764:.
741:.
733:.
725:.
715:17
713:.
682:.
678:.
655:.
643:.
620:.
608:.
596:^
586:.
582:.
563:.
544:.
494:44
492:.
488:.
451:^
437:.
429:.
417:.
396:}}
392:{{
380:.
368:.
364:.
288:.
155:.
112:,
108:,
75:.
27:,
978:.
960:.
930:.
918::
910::
893:.
873::
865::
849:.
829::
813:.
801::
784:.
772::
749:.
729::
721::
690::
684:1
663:.
651::
645:2
628:.
616::
610:8
588:2
529:.
508:.
506:.
500::
473:.
445:.
425::
419:8
402:)
376::
370:7
349:.
322:.
20:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.