그래프,graph - 그래프,graph
subgraph =,subgraph =,subgraph . subgraph
{
induced_subgraph
https://en.wikipedia.org/wiki/Induced_subgraph
induced_subgraph
subgraph =,subgraph =,subgraph . subgraph
{
induced_subgraph
https://en.wikipedia.org/wiki/Induced_subgraph
induced_subgraph
이상 cleanup ¶
Contents
- 1. 이상 cleanup
- 2. 세부분야들
- 3. (가장 중요한) 두 구성요소
- 4. 기타 graph의 components
- 5. 중요한 성질들
- 6. 그래프의 성질들? (아닌거 뺄 것)
- 7. 그래프의 종류들
- 7.1. undirected graph
- 7.2. directed graph, digraph
- 7.3. weighted graph
- 7.4. complete graph
- 7.5. planar graph
- 7.6. connected graph
- 7.7. biconnected graph
- 7.8. disconnected graph
- 7.9. empty graph / null graph
- 7.10. edgeless graph
- 7.11. singleton graph
- 7.12. complement graph
- 7.13. cycle graph
- 7.14. cyclic graph
- 7.15. butterfly graph = bowtie graph = hourglass graph
- 7.16. line graph
- 7.17. linear graph
- 7.18. path graph
- 7.19. complete graph
- 7.20. complete bipartite graph
- 7.21. bipartite graph
- 7.22. regular graph
- 8. Bmks ko
2. 세부분야들 ¶
algebraic_graph_theory =,algebraic_graph_theory . algebraic_graph_theory
{
대수적 그래프 이론 (wk)
algebraic graph theory
https://ko.wikipedia.org/wiki/대수적_그래프_이론
https://en.wikipedia.org/wiki/Algebraic_graph_theory
}
{
대수적 그래프 이론 (wk)
algebraic graph theory
https://ko.wikipedia.org/wiki/대수적_그래프_이론
https://en.wikipedia.org/wiki/Algebraic_graph_theory
}
4. 기타 graph의 components ¶
Component_(graph_theory)
}
"In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph."
= https://en.wikipedia.org/wiki/Component_(graph_theory)
= https://en.wikipedia.org/wiki/Component_(graph_theory)
... component component component= https://en.wikipedia.org/wiki/Component_(graph_theory)
= https://en.wikipedia.org/wiki/Component_(graph_theory)
}
5. 중요한 성질들 ¶
adjacency =,adjacency . adjacency
인접행렬,adjacency_matrix
adjacency
adjacency
kms : 인접행렬. via https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=adjacency
https://proofwiki.org/wiki/Definition:Adjacency_Matrix
graph의 자료구조/행렬,matrix 표현?
adjacencyhttps://proofwiki.org/wiki/Definition:Adjacency_Matrix
graph의 자료구조/행렬,matrix 표현?
adjacency
adjacency
6.2. centrality ¶
centrality =,centrality . centrality
{
번역?
'중심성' (incodom, wpko)
// not in kms as of 2022-11-14 => https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=centrality
{
번역?
'중심성' (incodom, wpko)
// not in kms as of 2022-11-14 => https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=centrality
대충 - 전체 graph에서 한 node(vertex)의 상대적 위치 관련한 measure로서, 얼마나 '중요한지' '중심에 서 있는지'에 대한?
각 node에 부여되는 수로 나타남? 표현됨?
대표적 측정법에는 연결정도중심성(degree_centrality)과 매개중심성(betweenness_centrality)이 있다.
다양한 측정법이 있으며 두 가지 - closeness_centrality and betweenness_centrality가 가장 많이 사용된다.[1]
방향성이 있어서
다양한 측정법이 있으며 두 가지 - closeness_centrality and betweenness_centrality가 가장 많이 사용된다.[1]
방향성이 있어서
- 내향중심성 in-centrality - ex. 연예인, 정치인처럼 가만히 있어도 주변에 사람이 몰리는. Prestige.
- 외향중심성 out-centrality - ex. 스스로 많은 사람들과 연결하고자 노력하는. Socialite.
6.6. sum ¶
graph_sum
{
합,sum
https://mathworld.wolfram.com/GraphSum.html
{
합,sum
https://mathworld.wolfram.com/GraphSum.html
두 adjacency_matrix의 값을 단순 덧셈해서 만든 그래프.
}7.2. directed graph, digraph ¶
directed graph, digraph
directed_graph
directed_graph
aka digraph
aka '방향 그래프' (wpko)
유향_그래프
Directed_graph = https://en.wikipedia.org/wiki/Directed_graph
aka '방향 그래프' (wpko)
유향_그래프
Directed_graph = https://en.wikipedia.org/wiki/Directed_graph
7.6. connected graph ¶
connected graph
연결그래프,connected_graph
{
https://mathworld.wolfram.com/ConnectedGraph.html
연결_그래프
connectivity or connectedness ? ... 아무튼 연결,connection
}
연결그래프,connected_graph
{
https://mathworld.wolfram.com/ConnectedGraph.html
연결_그래프
connectivity or connectedness ? ... 아무튼 연결,connection
}
7.7. biconnected graph ¶
biconnected graph
biconnected_graph =,biconnected_graph . biconnected_graph
https://mathworld.wolfram.com/BiconnectedGraph.html
Biconnected_graph = https://en.wikipedia.org/wiki/Biconnected_graph
biconnected_graph =,biconnected_graph . biconnected_graph
https://mathworld.wolfram.com/BiconnectedGraph.html
Biconnected_graph = https://en.wikipedia.org/wiki/Biconnected_graph
7.9. empty graph / null graph ¶
empty graph / null graph
empty_graph = null_graph ?
https://mathworld.wolfram.com/EmptyGraph.html
https://mathworld.wolfram.com/NullGraph.html
null_graph null_graph - curr at 널,null
empty_graph = null_graph ?
https://mathworld.wolfram.com/EmptyGraph.html
https://mathworld.wolfram.com/NullGraph.html
null_graph null_graph - curr at 널,null
7.10. edgeless graph ¶
edgeless graph
edgeless_graph
vertex는 가질 수 있지만 edge는 가지지 않는 그래프. (wpko)
무변_그래프 = https://ko.wikipedia.org/wiki/무변_그래프
edgeless_graph
vertex는 가질 수 있지만 edge는 가지지 않는 그래프. (wpko)
무변_그래프 = https://ko.wikipedia.org/wiki/무변_그래프
7.12. complement graph ¶
complement graph
complement_graph
번역
여 그래프(wpko)
rel. self-complementary_graph
여_그래프 = https://ko.wikipedia.org/wiki/여_그래프
https://mathworld.wolfram.com/GraphComplement.html
complement
complement_graph
번역
여 그래프(wpko)
rel. self-complementary_graph
여_그래프 = https://ko.wikipedia.org/wiki/여_그래프
https://mathworld.wolfram.com/GraphComplement.html
complement
7.13. cycle graph ¶
cycle graph
cycle_graph
순환그래프?
Compare: graph_cycle
순환,cycle?
https://mathworld.wolfram.com/CycleGraph.html
https://en.wikipedia.org/wiki/Cycle_graph
cycle_graph
순환그래프?
Compare: graph_cycle
순환,cycle?
https://mathworld.wolfram.com/CycleGraph.html
https://en.wikipedia.org/wiki/Cycle_graph
-> aka circular_graph
!= cyclic_graph
!= cyclic_graph
7.15. butterfly graph = bowtie graph = hourglass graph ¶
butterfly graph = bowtie graph = hourglass graph
butterfly_graph = bowtie_graph = hourglass_graph
{
bowtie_graph hourglass_graph
//wpen: (also called the bowtie graph and the hourglass graph)
butterfly_graph = bowtie_graph = hourglass_graph
{
bowtie_graph hourglass_graph
//wpen: (also called the bowtie graph and the hourglass graph)
7.16. line graph ¶
line_graph =,line_graph . line_graph
line_graph
https://en.wikipedia.org/wiki/Line_graph
path_graph, linear_graph와 다름.
line_graph
https://en.wikipedia.org/wiki/Line_graph
path_graph, linear_graph와 다름.
7.22. regular graph ¶
"는 모든 꼭짓점이 동일한 수의 이웃을 가지는 그래프이다. 즉, 모든 꼭짓점이 같은 차수" (wk)
Sub:
cubic_graph : 3-regular graph
https://mathworld.wolfram.com/RegularGraph.html
https://ko.wikipedia.org/wiki/정규_그래프
https://en.wikipedia.org/wiki/Regular_graph
cubic_graph : 3-regular graph
https://mathworld.wolfram.com/CubicGraph.html
https://en.wikipedia.org/wiki/Cubic_graph
strongly_regular_graphhttps://en.wikipedia.org/wiki/Cubic_graph
aka "trivalent graphs"
https://en.wikipedia.org/wiki/Strongly_regular_graph
https://mathworld.wolfram.com/StronglyRegularGraph.html
weakly_regular_graphhttps://mathworld.wolfram.com/StronglyRegularGraph.html
https://mathworld.wolfram.com/RegularGraph.html
https://ko.wikipedia.org/wiki/정규_그래프
https://en.wikipedia.org/wiki/Regular_graph
ADDHERE (graphs)
8. Bmks ko ¶
이산수학 : Richard Johnsonbaugh 저서 (1999) Page 363~373 excerpt
http://www.aistudy.com/math/graph_johnsonbaugh.htm
http://www.aistudy.com/math/graph_johnsonbaugh.htm
Twins:
----
- [1] http://www.incodom.kr/Betweenness_Centrality
- [2] http://www.incodom.kr/Centrality
- [3] 중심성
- [4] 중심성
- [5] 중심성
- [6] 중심성
- [7] Path_graph "a path graph (or linear graph) is a graph whose vertices can be listed in the order..."