???? Graph Structure

About This Presentation

Title:

???? Graph Structure

Description:

Title: Artificial Intelligence AI Author: pluto Last modified by: pluto Created Date: 1/13/2006 11:57:52 AM Document presentation format: – PowerPoint PPT presentation

Number of Views:27

Avg rating:3.0/5.0

Slides: 30

Provided by: plu84

Category:

more less

Transcript and Presenter's Notes

Title: ???? Graph Structure

1
????Graph Structure

chapter 9

2
???????

??????????
??????,?????????,?????????,????????

?????(Eular)?????
????(Vertices)???????,?(Edge)???????
???????????????,??????????,???????,????????

4
??

Graph
???(Vertices)??(Edges)???
?G(V,E)???
V????????,E???????
????(Undirected Graph)
?(Edges)???????
?(V1,V2)??(V2,V1)????
????(Directed Graph)
?(Edges)??????
?ltV1,V2gt??ltV2,V1gt?????

5
???? ?(A)? ?????,??(Vertices)??(Edges)
?? V(G)A,B,C,D,E E(G)(A,B),(A,C),(B,A),(B,D)
,(C,A),(C,E),(D,B) ,(D,E) ,(E,C) ,(E,D) ?(B)?
?????,??(Vertices)??(Edges) ?? V(G)A,B,C,D,E E
(G)ltA,Bgt,ltA,Cgt,ltB,Dgt,ltC,Egt,ltD,Egt
6
????????????

???? ( complete graph )
????????,??n???,?????n(n-1)/2??,?????????
????????,??n???,?????n(n-1)??,????????

?? ( path )
???,??????????????
??(A)?,A?E????(A,B), (B,E)?(A,C),
(C,E)?(A,B),(B,D),(D,E)?
????(simple path)
???????(cycle,????)
(A,B),(B,D),(D,E),(E,C),(C,A)???????A,??????????

????(Path Length)
???? k ???????(Edge)???
??(subgraph)
? G(V,E) ? G(V,E) ???,?V?V?E?E

??(Connected)
??????,???Vi???Vj?????,?Vi?Vj????
????(Connected Graph)
????G?,?????????,??????????,?????????
????(Connected Component)
?????????(Maximal Connected Subgraph),??????2?????

????(Strongly Connected)
?????(Directed Graph)??,?????ltVi,Vjgt ??????? Vi ?
Vj ??????????Vj? Vi???(Directed Graph)
??(Adjacent)
???? u,v?V,(u,v)?E,??? u ??? v ??
??????????

???(Degree)
????? u ??????? u ?????,??9-3??(A)?A???????2
???G(V,E)
???? ( in - degree )??????v????????????9-3??(B)?,
A ????????0,?E????????2
???? ( out - degree )?????????,???????v??????????
??9-3??(B)?,A????????2,?E????????0

12
??????