Week 10: Graphs, Trees, and Matrices
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# Week 10: Graphs, Trees, and Matrices > **Course:** Jan 2026 - Mathematics I > **Focus:** Graph theory basics and the data structures that naturally appear with it. --- ## 1.
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Week 10: Graphs, Trees, and Matrices
Course: Jan 2026 - Mathematics I Focus: Graph theory basics and the data structures that naturally appear with it.
1. Core idea
Week 10 is about encoding graph structure and reading graph behavior from degrees, matrices, and traversal order.
What to remember
- In a simple graph, the adjacency matrix has zeros on the diagonal.
- Maximum non-zero entries happen when every possible edge exists.
- A BFS tree reveals layers from the root.
- A stack fits depth-first backtracking.
- A queue fits breadth-first exploration.
2. Common traps
- Counting matrix entries without respecting symmetry.
- Mixing up BFS and DFS behavior.
- Treating a valid degree sequence as if every ordering were valid.
3. Speedrun pattern
When you see a Week 10 question, ask:
- Is this asking about representation or traversal?
- What graph invariant is being tested?
- Which data structure matches the process?