Week 8 — adjacency & labelled graphs

Quiz 2 scope: Weeks 1–8 per IITM May 2026 foundation courses. Source baseline: IITM BS admissions important-dates calendar · May 2026 cycle. Times on assessments are operational conventions — verify hall ticket.

Week map

Classify → Represent → Execute → Trap-check

• Recognize: Ask: How fill matrix from edge list?
• Procedure: Zero matrix; for each edge (u,v,w) set M[u][v]=w (and M[v][u] if undirected).
• Variations / traps: Watch for: Off-by-one vertex numbering (1..n vs 0..n-1).

Formula chain (compressed)

labelled edges → matrix stores weight/label → switch list ↔ matrix.

1. Labelled edge — edge (u,v,w) — weight or name w
2. Matrix entry — M[u][v] = label or 0 — no edge = sentinel
3. Directed — M[u][v] ≠ M[v][u] — one-way edges
4. Representation switch — list ↔ matrix — same graph, two views
5. Self-loop — M[i][i] nonzero? — check diagonal

Deep study

Computational Thinking · Week 8 — Labelled adjacency graphs

Week map

Labelled edge notation

• Label → data on edge → weight, distance, time, capacity.
• Weighted graph → each edge has numeric label → often non-negative in intro problems.
• $M[i][j] = w$ → edge from $i$ to $j$ has weight $w$.
• $M[i][j] = 0$ or $\infty$ → no edge (convention varies — read problem statement).

text
     1 --4-- 2
      \       |
       10     2
        \     |
         ---- 3

Weight matrix

text
W = [ 0  4 10]
    [ ∞  0  2]
    [ ∞  ∞  0]

Adjacency list with labels

text
0 → [(1, 4), (2, 10)]
1 → [(2, 2)]
2 → []

Directed vs undirected weights

Pattern families

Easy — Read label from diagram

Medium — Build weight matrix

Hard — Compare path totals

Worked mini-examples

text
W[0][1]=3, W[1][2]=5, others missing

Traps

• Confusing “no edge” 0 with “zero weight” edge — problem defines convention.
• Forgetting directed orientation when summing path.
• Double-counting undirected edge in degree/weight tally.
• Picking edge with min label locally vs min total path.
• Vertex label mismatch with matrix index.

Diagnostic (try yourself)

1. Weighted edge from X to Y is 6. In matrix with X=1, Y=2, what is $W[1][2]$?
2. Path A→B→C with weights 3 and 5. Total weight?
3. Undirected edge weight 4 between vertices 0 and 2. What are $W[0][2]$ and $W[2][0]$?
4. Adjacency list for vertex 1 is [(2, 7), (3, 1)]. What is weight of edge 1→3?
5. Direct path weight 12 vs two-hop path 4+5. Which route is cheaper?

ChatGPT prep archive

• Chatty reference archive

Archived import for extra depth — complements the notes above, not official IITM material.

Core concepts

• Adjacency matrix: n×n for n vertices; entry labels edge or 0/absent.
• Labelled graph: edges carry names/weights/distances—not just on/off.
• Switch representation: same graph as edge list or matrix; convert by filling cells.
• Sparse vs dense: matrix fine small n; list of pairs for few edges.

Notation & vocabulary

Pattern families

Easy — Fill adjacency matrix

Medium — Read label

Hard — Convert representations

Drill these on the pattern atlas — filter to week 8.

Traps

• Off-by-one vertex numbering (1..n vs 0..n-1).
• Missing reverse edge in undirected fill.
• Label 0 confused with no edge.
• Matrix size not matching vertex count.

Retrieval prompts

1. How fill matrix from edge list?
2. What is labelled edge?
3. When matrix vs edge list?

Practice loop

1. Read Deep study (if present) or core concepts once.
2. Recite the formula chain without looking.
3. Open one easy pattern on the interactive atlas for week 8.
4. Attempt without solutions; mark studied after an honest try.
5. Say one trap aloud before closing the tab.

Related

• Full weeks 1–8 prep guide
• Pattern atlas note
• Formula chain desk