Graphs
A graph data structure is a collection of nodes that have data and are connected to other nodes.
Let's try to understand this through an example. On facebook, everything is a node. That includes User, Photo, Album, Event, Group, Page, Comment, Story, Video, Link, Note...anything that has data is a node.
Every relationship is an edge from one node to another. Whether you post a photo, join a group, like a page, etc., a new edge is created for that relationship.
More precisely, a graph is a data structure (V, E) that consists of
A collection of vertices V
A collection of edges E, represented as ordered pairs of vertices (u,v).
Graph Terminology:
* Adjacency: A vertex is said to be adjacent to another vertex if there is an edge connecting them. Vertices 2 and 3 are not adjacent because there is no edge between them.
* Path: A sequence of edges that allows you to go from vertex A to vertex B is called a path. 0-1, 1-2 and 0-2 are paths from vertex 0 to vertex 2.
* Directed Graph: A graph in which an edge (u,v) doesn't necessarily mean that there is an edge (v, u) as well. The edges in such a graph are represented by arrows to show the direction of the edge.
Graph Representation:
Graphs are commonly represented in two ways:
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Graph Data Stucture
In this tutorial, you will learn what a Graph Data Structure is. Also, you will find representations of a graph.
A graph data structure is a collection of nodes that have data and are connected to other nodes.
Let's try to understand this through an example. On facebook, everything is a node. That includes User, Photo, Album, Event, Group, Page, Comment, Story, Video, Link, Note...anything that has data is a node.
Every relationship is an edge from one node to another. Whether you post a photo, join a group, like a page, etc., a new edge is created for that relationship.
graph data structure explained using facebook's example. Users, groups, pages, events, etc. are represented as nodes and their relationships - friend, joining a group, liking a page are represented as links between nodes
Example of graph data structure
All of facebook is then a collection of these nodes and edges. This is because facebook uses a graph data structure to store its data.
More precisely, a graph is a data structure (V, E) that consists of
A collection of vertices V
A collection of edges E, represented as ordered pairs of vertices (u,v)
a graph contains vertices that are like points and edges that connect the points
Vertices and edges
In the graph,
V = {0, 1, 2, 3}
E = {(0,1), (0,2), (0,3), (1,2)}
G = {V, E}
Graph Terminology
Adjacency: A vertex is said to be adjacent to another vertex if there is an edge connecting them. Vertices 2 and 3 are not adjacent because there is no edge between them.
Path: A sequence of edges that allows you to go from vertex A to vertex B is called a path. 0-1, 1-2 and 0-2 are paths from vertex 0 to vertex 2.
Directed Graph: A graph in which an edge (u,v) doesn't necessarily mean that there is an edge (v, u) as well. The edges in such a graph are represented by arrows to show the direction of the edge.
Graph Representation
Graphs are commonly represented in two ways:
1. Adjacency Matrix:
An adjacency matrix is a 2D array of V x V vertices. Each row and column represent a vertex.
If the value of any element a[i][j] is 1, it represents that there is an edge connecting vertex i and vertex j.
2. Adjacency List
An adjacency list represents a graph as an array of linked lists.
The index of the array represents a vertex and each element in its linked list represents the other vertices that form an edge with the vertex.
Graph Operations
The most common graph operations are:
* Check if the element is present in the graph
* Graph Traversal
* Add elements(vertex, edges) to graph
* Finding the path from one vertex to another
