Graph Theory Fundamentals
Graph theory studies networks of connected objects. A graph consists of vertices, also called nodes, and edges, which are connections between nodes. This mathematical structure models relationships in computer networks, social networks, transportation systems, and biological networks.
Types of Graphs
Undirected Graph: Edges have no direction. Connections are bidirectional.
Directed Graph: Edges have direction. Connections flow in one direction.
Weighted Graph: Edges have associated weights or costs representing distance, time, or other metrics.
Simple Graph: No loops or multiple edges between the same pair of vertices.
Complete Graph: Every pair of vertices is connected by an edge.
Bipartite Graph: Vertices can be divided into two disjoint sets with edges only between sets.
Applications
Computer Networks: Routing protocols, network topology analysis, bandwidth optimization.
Social Networks: Friendship graphs, influence analysis, community detection.
Transportation: Road networks, flight routes, logistics optimization.
Biology: Protein interaction networks, phylogenetic trees, metabolic pathways.
Web Graphs: Page ranking algorithms, link analysis, search engine optimization.
Scheduling: Task dependencies, resource allocation, project management.
