Graphs are used to represent connected objects, such as routers in a network or people on a social media platform.

They consist of nodes and edges, where a node is also called a vertex.

GRAPHS

• Tree vs Graph: A tree is a kind of graph without any cycles, and it has a root node. In contrast, a graph can have cycles and does not have a root node.

  

• Nodes and Edges: Nodes are connected by edges, which represent relationships or connections between the nodes. Nodes can have any number of connections or edges.

• Adjacency: Nodes that are directly connected by an edge are called adjacent or neighbours. For example, John and Bob are adjacent in a graph.

  

• Directed vs Undirected Graphs: In a directed graph, edges have a direction, indicating a one-way relationship. In an undirected graph, edges have no direction, representing mutual relationships.

Directed Graph

Undirected Graph

• Weights: Edges in a graph can have weights, which represent the strength or importance of the connection between nodes. Weights can be used to determine the significance of relationships, such as in social media platforms.

Applications

• Social Networks: Graphs represent connections between users, with weights indicating interaction frequency.
• Shortest Path Finding: Graphs model connections between cities or areas, with weights representing distance or travel cost. Algorithms can find the shortest path between two nodes.
• Understanding graphs is essential for various applications, from analyzing social networks to optimizing transportation routes. Graphs offer a versatile way to represent and analyze interconnected data structures.