What is Graph?

A graph is a non-linear data structure that represents a collection of interconnected nodes or vertices. It consists of a set of vertices and a set of edges, where each edge connects a pair of vertices.

Example: Consider two locations connected by road. Each location is a vertex and the road connection between them form the edges.

Graph is represented by G(V,E) where V is set of vertices and E is the set of edges.

Why do we need graphs?

• Modelling Complex Relationships: Many real-world systems involve complex relationships and dependencies between entities. Graphs allow to represent these relationships explicitly, enabling a better understanding and analysis.

Example: Facebook represents friendships between users as a graph, allowing for friend suggestions and analyzing social connections.

• Efficient Data Representation: Graphs provide a compact and efficient representation of relationships. Rather than storing explicit connections between all pairs of entities, graphs store the vertices and edges, allowing for efficient storage and retrieval of information.

Example: - Web Graph: The internet can be represented as a graph where web pages are vertices, and hyperlinks are edges.

• Algorithmic Solutions: Graph algorithms have been extensively developed and studied, making it easier to solve various computational problems efficiently. Graph algorithms can be used to find shortest paths, detect cycles, perform network analysis, identify clusters, and much more.

Example: Shortest Path: Dijkstra's algorithm is used to find the shortest path between two locations in a transportation network, such as finding the fastest route between two cities.

• Network Analysis: Graphs are particularly useful for analyzing networks. By representing connections as edges, we can study properties like centrality, connectivity, clustering, and community structure. This information is valuable for understanding social networks, transportation systems, information networks, and more.

Example: Transportation Network Analysis: Graph algorithms can be applied to analyze traffic flow, optimize routing, or identify critical nodes or links in a transportation network.

• Recommendation Systems: Graph-based models and algorithms are commonly used in recommendation systems. By analyzing the graph structure of connections between users, products, or items, personalized recommendations can be generated based on similar preferences, behaviors, or relationships.

Example: Movie Recommendations: By analyzing the graph of user ratings and movie connections, recommendation systems like those used by Netflix suggest movies based on similar viewing patterns.

• Data Visualization: Graphs can be visualized to gain insights into complex data. Visualization techniques help in understanding patterns, identifying outliers, and exploring the relationships between entities more intuitively.

Example: Network Traffic Visualization: Graph-based visualizations help monitor and analyze network traffic patterns, identifying anomalies or bottlenecks in computer networks.