Real World Applications

[!NOTE] Graphs are not just for interviews. They run the world.

1. The Internet: PageRank (Google)

How does Google know which website is most important?

  • The Web: A massive directed graph.
  • Nodes: Pages.
  • Edges: Hyperlinks.
  • Idea: A page is important if important pages link to it. It’s a popularity contest where votes are weighted.

2. Social Networks (Facebook/LinkedIn)

  • The Graph: Massive undirected (Friends) or directed (Followers) graph.
  • Features:
  • “People You May Know”: Triangle Closing. If A knows B, and B knows C, suggest A knows C.
  • Degrees of Separation: BFS to find how far you are from Kevin Bacon.

3. Uber/Lyft: Routing

  • The Graph: The entire road network.
  • Nodes: Intersections.
  • Edges: Road segments (Weighted by distance + real-time traffic).
  • Challenge: The graph changes every second (traffic jams, accidents).
  • Algorithm: Contraction Hierarchies (Advanced Dijkstra).

4. Interactive: PageRank Simulator

Simulate the flow of “Importance” (Probability).

  • Start with equal importance.
  • In each step, a node passes its importance evenly to its neighbors.
  • Watch how nodes with many incoming links (or links from important nodes) grow larger.
Step: 0

5. Deep Dive Strategy Lab: Use Cases

Intuition Through Analogy

Think of this chapter like city route planning. The goal is not to memorize a fixed trick, but to repeatedly answer:

  1. What is the bottleneck?
  2. Which constraint dominates (time, memory, latency, correctness)?
  3. Which representation makes the bottleneck easier to eliminate?