Структура данных графа и Algorithms (Пример)
Сара Чен
⚡ Умное резюме
Graph Data Structure is a non-linear collection of vertices and edges where each edge links a pair of vertices. Graphs model real-world networks such as maps, social connections, and web pages, and support many powerful algorithms.
Что такое граф в структуре данных?
A graph is a non-linear data structure that consists of vertices and edges, where vertices contain the information or data, and the edges work as a link between a pair of vertices.
It is used to solve real-world problems like finding the best route to the destination location and the route for telecommunications and social networks. Users are considered a node in the Graph, and the wires are the edges connecting the users.
Если ребра представлены как E, а вершины представлены как V, то граф G можно записать как набор вершин и ребер, например G (V, E).
Пример графика в структуре данных
Here is a simple example of a graph data structure:
It is a simple undirected graph (one kind of Graph). Here the set of vertices is: {A, B, C, D, E, F}. Two vertices create an edge. For example, A and B are linked with an edge. However, A and F are not linked with any edges.
Графовая терминология в структуре данных
The following are some important terms used in the graph data structure:
| Срок | Описание |
|---|---|
| Вершина | Each data element is called a vertex or a node. In the above image, A, B, C, D & E are the vertices. |
| Край (Дуга) | Connecting links between two nodes or vertices are called an edge (Arc). It has two ends and is represented as (startingVertex, endingVertex). |
| Ненаправленный край | Это двунаправленный край. |
| Направленный край | Это однонаправленная грань. |
| Взвешенное преимущество | An edge with a value on it. |
| Степень | In a Graph, the number of edges connected to a vertex is called a degree. |
| Инградус | Общее количество входящих ребер, соединенных с вершиной. |
| Выходящая степень | Общее количество исходящих ребер, соединенных с вершиной. |
| Автопетля | Ребро называется петлей, если две его конечные точки совпадают. |
| Смежность | Vertices are said to be adjacent if an edge is connected between them. |
Типы графов в структуре данных
Вот список наиболее распространенных типы графиков в структуре данных:
- Направленный график
- Ненаправленный граф
- Взвешенный график
- Двунаправленный граф
- Бесконечный граф
- Нулевой график
- Тривиальный граф
- Мультиграф
- Полный график
- Связанный граф
- Циклический график
- Направленный ациклический граф (DAG)
- График цикла
- Двудольный граф
- Граф Эйлера
- График Гамильтона
How to Represent a Graph in Data Structure?
A graph is commonly stored in memory using one of two representations. The choice affects how much memory the graph uses and how fast common operations run.
- Матрица смежности: A two-dimensional V × V array where cell [i][j] is 1 (or the edge weight) if an edge exists between vertex i and vertex j, and 0 otherwise. It allows O(1) edge lookup but uses O(V²) space, making it best for dense graphs.
- Список смежности: An array of lists where each vertex stores a list of its neighbouring vertices. It uses O(V + E) space and is efficient for sparse graphs, which is why most real-world graphs use it.
You can read more about these in the adjacency list and matrix representation of a graph учебное пособие.
Применение структуры данных графа
A graph has many use cases. There are a lot of algorithms that use Graphs. Here are some of the applications of the Graph:
- Google Maps uses graphs to find the intersection of two roads and calculate the distance between two locations. For example, Дейкстра, for finding the shortest distance between the source and destination location.
- Facebook uses Graphs to find the mutual friends of the users. Its algorithm considers each user as a node of a graph.
- For resource allocation, a DAG (Directed Acyclic Graph) is used. It checks the dependency of the resources.
- Google Поисковые системы используют графы для ранжирования веб-сайтов.
- Картаping Устройство использует структуру данных типа граф.
- A Маршрутизатор and its protocol use the Graph to learn the path to the destination.
