이상 cleanup ¶

2. 세부분야들 ¶

3. (가장 중요한) 두 구성요소 ¶

4. 기타 graph의 components ¶

graph의 component
graph_component
component
{
성분 ? - 성분,component page exists
요소 ?

rel.
connected_component =,connected_component . connected_component
{
connected component
연결 성분

연결,connection
... connected.component
}

---

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
}

5. 중요한 성질들 ¶

adjacency =,adjacency . adjacency

adjacency

인접행렬,adjacency_matrix

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?

adjacency
adjacency

adjacency

---

연결,connection

6. 그래프의 성질들? (아닌거 뺄 것) ¶

6.1. connectivity 연결성? ¶

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

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

• 내향중심성 in-centrality - ex. 연예인, 정치인처럼 가만히 있어도 주변에 사람이 몰리는. Prestige.
  
• 외향중심성 out-centrality - ex. 스스로 많은 사람들과 연결하고자 노력하는. Socialite.
  

이런 두 가지가 있다.

http://www.incodom.kr/Centrality
중심성
Centrality
}

6.2.1. degree centrality ¶

degree_centrality =,degree_centrality . degree_centrality
{
번역?
연결정도중심성[2]
연결중심성[3]

가장 간단한 (centrality?) 측정법.

degree_centrality x 2023-08-20

http://www.incodom.kr/Degree_Centrality
}

6.2.2. closeness = closeness centrality ¶

closeness = closeness_centrality
{
번역?
근접중심성[4]

tmp videos ko
https://www.youtube.com/watch?v=iB5T0vFypNQ

http://www.incodom.kr/Closeness_Centrality
Centrality#Closeness_centrality
Closeness_centrality

Closeness.Centrality
}

6.2.3. betweenness = betweenness centrality ¶

betweenness = betweenness_centrality
{
번역?
매개중심성[5]

http://www.incodom.kr/Betweenness_Centrality
Betweenness_centrality = https://en.wikipedia.org/wiki/Betweenness_centrality

Up: 중심성,centrality
}

6.2.4. eigenvector centrality ¶

6.3. weight ¶

가중값,weight
{
가중값,weight
그래프를 시각화할 때 weight를 edge의 굵은 정도로 나타내는 경우가 많다.
}

6.4. distance ¶

graph_distance
{
Distance_(graph_theory)
거리,distance
}

6.5. diameter ¶

6.6. sum ¶

6.7. difference ¶

6.8. join ¶

6.9. union ¶

6.10. cycle ¶

7. 그래프의 종류들 ¶

7.1. undirected graph ¶

7.2. directed graph, digraph ¶

directed graph, digraph
directed_graph

aka digraph
aka '방향 그래프' (wpko)

유향_그래프
Directed_graph = https://en.wikipedia.org/wiki/Directed_graph

7.3. weighted graph ¶

weighted graph
weighted_graph =,weighted_graph . weighted_graph
{
가중값,weight - 가중값,weight
}

7.4. complete graph ¶

complete graph
완전그래프,complete_graph - 완전그래프,complete_graph

7.5. planar graph ¶

planar graph
평면그래프,planar_graph - 평면그래프,planar_graph

7.6. connected graph ¶

connected graph
연결그래프,connected_graph
{
https://mathworld.wolfram.com/ConnectedGraph.html
연결_그래프

= https://ko.wikipedia.org/wiki/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

7.8. disconnected 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

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

7.11. singleton graph ¶

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

7.13. cycle graph ¶

7.14. 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)

성질
평면그래프,planar_graph
undirected_graph
5 vertexes
6 edges

https://mathworld.wolfram.com/ButterflyGraph.html
Butterfly_graph

= https://en.wikipedia.org/wiki/Butterfly_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.

7.17. linear graph ¶

linear_graph
linear_graph x
linear graph
이건 직선 그래프를 뜻하기도 하고(일차함수), path graph(아래)를 뜻하기도 한다.[7]

7.18. path graph ¶

path_graph x
https://en.wikipedia.org/wiki/Path_graph
path graph
경로,path
linear_graph 라고 하기도 한다.

7.19. complete graph ¶

https://en.wikipedia.org/wiki/Complete_graph
complete graph
https://ko.wikipedia.org/wiki/완전_그래프
완전그래프,complete_graph

7.20. complete bipartite graph ¶

https://ko.wikipedia.org/wiki/완전_이분_그래프
https://en.wikipedia.org/wiki/Complete_bipartite_graph
complete bipartite graph

7.21. bipartite graph ¶

bipartite graph

7.22. regular graph ¶

8. Bmks ko ¶

이산수학 : Richard Johnsonbaugh 저서 (1999) Page 363~373 excerpt
http://www.aistudy.com/math/graph_johnsonbaugh.htm

---

Twins:

그래프_이론
= https://ko.wikipedia.org/wiki/그래프_이론

Graph_theory
= https://simple.wikipedia.org/wiki/Graph_theory

Graph_theory

グラフ理論

https://proofwiki.org/wiki/Definition:Graph_Theory

https://everything2.com/title/graph theory

https://www.britannica.com/topic/graph-theory