Testing

Structure

Tests mirror the llm-chat convention:

tests/
├── index.ts            # barrel
├── helper/
│   └── graph.ts        # topology builders + test utilities
└── unit/
    ├── add.test.ts
    ├── remove.test.ts
    ├── clear.test.ts
    ├── size.test.ts
    └── rank/
        ├── basic-flow.test.ts
        ├── edge-cases.test.ts
        ├── invariants.test.ts
        ├── parameters.test.ts
        ├── topologies.test.ts
        └── academic.test.ts

Coverage

100% required on statements, branches, functions, and lines — enforced via Vitest config. The src/index.ts barrel export is excluded from the threshold.

Invariants checked in every rank test

• Sum ≈ 1: rankSum(result) is within 1e-10 of 1
• All positive: every node score > 0
• No NaN/Infinity: Number.isFinite on every value
• Determinism: repeated calls to rank() return identical results
• Edge mutations between calls: interleaved add/rank are independent

Academic reference graphs

The implementation is validated against exact solutions and published reference values from four authoritative sources. All graphs are defined inline via fromEdges() in tests/unit/rank/academic.test.ts.

Oregon State University — Math 390R/490R

Source: PageRank worked example (PDF)

1 → 2, 1 → 3, 1 → 4
2 → 3, 2 → 4
3 → 4
4 → 1

No dangling nodes.

Damping	PageRank vector (exact rational)	Decimal
d = 1	[6/17, 2/17, 3/17, 6/17]	≈ [0.3529, 0.1176, 0.1765, 0.3529]
d = 2/3	[201/652, 99/652, 132/652, 220/652]	≈ [0.3083, 0.1518, 0.2025, 0.3374]

BYU ACME Lab — Problem 2 (unweighted)

Source: The PageRank Algorithm — ACME Labs, Fig 1

a → b, a → c, a → d
c → b, c → d
d → c

Node b is dangling (no outgoing edges).

Damping	Reference (Problem 2, itersolve)
d = 0.85	{a: 0.095758635, b: 0.274158285, c: 0.355924792, d: 0.274158285}

BYU ACME Lab — Weighted graph (Fig 3)

Source: The PageRank Algorithm — ACME Labs, Fig 3 / NetworkX example

a → b (w=2), a → c (w=1), a → d (w=1)
c → b (w=1), c → d (w=2)
d → c (w=2)

Node b is dangling.

Damping	Reference (nx.pagerank, alpha=0.85)
d = 0.85	{a: 0.0858848438, b: 0.2276927427, c: 0.3716732339, d: 0.3147491797}

MathWorks MATLAB — 6-node example

Source: Use PageRank Algorithm to Rank Websites — MathWorks docs

alpha → beta, alpha → epsilon
beta → gamma, beta → delta
gamma → delta, gamma → epsilon, gamma → zeta
delta → alpha
epsilon → alpha

Node zeta is dangling.

Damping	Reference (centrality(G,'pagerank','FollowProbability',0.85))
d = 0.85	{α: 0.32098, β: 0.17057, γ: 0.10657, δ: 0.13678, ε: 0.20078, ζ: 0.06432}

Ring of 10 at d = 1

Exact uniform distribution: every node receives 0.1. No dangling nodes, so d = 1 converges immediately to the uniform eigenvector.

Topology & parameter sweep

Additional test graphs exercise specific structural properties:

Topology	Description
Ring (10 nodes)	Uniform ranks at any damping
Star (center → 8 leaves)	Hub-and-spoke
Bipartite (3 → 4)	Two-tier structure
Two-tier hub (3 mids × 4 leaves)	Depth-3 fan-out
Dense (20 nodes, ~60% edges)	Near-complete graph
Chain (100 nodes)	Long sequential path

Parameter tests vary damping (0.5, 0.85, 0.99), maxIter (1, 500, 2000), and tol (1e-6, 1e-10, 1e-12) to verify convergence behaviour across the full operating range.