> For the complete documentation index, see [llms.txt](https://pyohamen.gitbook.io/til/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://pyohamen.gitbook.io/til/algorithm/data_structure/graph.md).

# Graph

> A Graph consists of a finite set of **vertices (or nodes)** and set of **Edges** which connect a pair of nodes.

![](https://www.fun-coding.org/00_Images/graph.png)

## Terms

> Mathematical graphs can be represented in data structure. We can represent a graph using an array of vertices and a two-dimensional array of edges. Before we proceed further, let's familiarize ourselves with some important terms

* **Vertex ( Node )**

  : Each **node** of the graph is represented as a **vertex**. In the following example, the labeled circle represents **vertices**. Thus, A to G are **vertices**. We can represent them using an array as shown in the following image. Here A can be identified by index 0. B can be identified using index 1 and so on.
* **Edge**

  : represents a path between two **vertices** or a **line** between two **vertices**. In the following example, the lines from A to B, B to C, and so on represents **edges**. We can use a two-dimensional array to represent an array as shown in the following image. *Here AB can be represented as 1 at row 0, column 1, BC as 1 at row 1, column 2 and so on, keeping other combinations as 0.*
* **Adjacency**

  : Two **node** or **vertices** are **adjacent** if they are connected to each other through an **edge**. In the following example, B is **adjacent** to A, C is **adjacent** to B, and so on.
* **Path**

  : Path represents a sequence of **edges** between the two **vertices**. In the following example, ABCD represents a **path** from A to D.

![](https://www.tutorialspoint.com/data_structures_algorithms/images/graph.jpg)

* **Reference terms**

  > 아직까지 필요해본적이 없음

  * **정점의 차수 ( Degree )**: 무방향 그래프에서 하나의 정점에 인접한 정점의 수
  * **진입 차수 ( In-Degree )**: 방향 그래프에서 외부에서 오는 간선의 수
  * **진출 차수 ( Out-Degree )**: 방향 그래프에서 외부로 향하는 간선의 수
  * **경로 길이 ( Path Length )**: 경로를 구성하기 위해 사용된 간선의 수
  * **단순 경로 ( Simple Path )**: 처음 정점과 끝 정점을 제외하고 중복된 정점이 없는 경로
  * **사이클 ( Cycle )**: 단순 경로의 시작 정점과 종료 정점이 동일한 경우

## Implementation

```python
'''
Here A can be identified by index 0. B can be identified using index 1 and so on.
'''
graph = [
    [1, 4, 5],
    [0, 2],
    [1, 3],
    [2],
    [0],
    [0, 6],
    [5]
]
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://pyohamen.gitbook.io/til/algorithm/data_structure/graph.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.