Graph Applications

Social Networks

Social networks are modeled as graphs where people are vertices and friendships are edges. This enables analysis of communities, influence, and connections.

Applications:
  Friend recommendations (friends of friends)
  Community detection (clusters)
  Six degrees of separation
  Influencer identification (high degree centrality)

Transportation Networks

Roads, flights, railways as graphs:
  Vertices: Cities or intersections
  Edges:    Roads or flights
  Weights:  Distance, time, or cost

Algorithms:
  Shortest path: Dijkstra's algorithm
  Minimum spanning tree: Kruskal's or Prim's
  Route optimization: Traveling salesman problem

Computer Networks

Internet and network infrastructure:
  Vertices: Routers, switches, computers
  Edges:    Physical or logical connections

Key problems:
  Routing: Finding best path for data packets
  Reliability: Ensuring connectivity despite failures
  Load balancing: Distributing traffic across paths

Other Applications

Dependency Graphs:
  Software dependencies, task scheduling
  Topological sort determines execution order

Map Coloring:
  Adjacent regions must have different colors
  Four Color Theorem: 4 colors suffice for planar maps

Recommendation Systems:
  Bipartite graphs of users and products
  Collaborative filtering based on graph patterns

Biological Networks:
  Protein interactions, food webs, neural networks