Graphs :

Graph :

• A graph is a non-linear data structure that can be looked at as a collection of vertices (or nodes) potentially connected by line segments named edges.

Vertex :

• or node means the data object that can has other adjacent vertices or not.a vertex (plural vertices) or node is the fundamental unit of which graphs are formed.

Edge :

• the connection between two nodes.

Degree :

• number of edges that the node has.

Neighber :

• the connected nodes to the node.

Directed & unDirected Graph

• Directed or called Digraph : that the edge has a direction and one of two connected nodes has the other, and the other one hasn’t. (uni-directional)

• unDirected : both of them has the other node. (bi-directional)

complete graph :

• when each node connected to all other nodes.

connected :

• when no node doesn’t has least one edge or doesn’t connected at least to one node.

Dusconnected graph :

• when one or more nodes doesn’t has any edge or node.

directed acyclic graph is also called a DAG :

• when no cycle happen in the graph.

Cyclic Graphs :

• when starts with node and returns to the same node.

Weighted Graphs :

• A weighted graph is a graph with numbers assigned to its edges. These numbers are called weights.

We represent graphs through:

- Adjacency Matrix : by two dimensional array.
- Adjacency List : it is a collection of linked lists or array that lists all of the other vertices that are connected.

• in weighted graphs you must include both the weight and the name of the adjacent vertex.

Traversals :

• will do traversals in graph with breadth first and depth first methods.

  
  

Real applications of graphs :

1. GPS and Mapping

2. Driving Directions

3. Social Networks

4. Airline Traffic

5. Netflix uses graphs for suggestions of products

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