Graph Theory Calculator

Analyze a small weighted undirected graph for connectivity, shortest paths, MST, coloring, and traversal properties.

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Introduction to Graph Theory (Trudeau) - A friendly, inexpensive Dover introduction to graphs and networks.

What This Calculator Does

This calculator analyzes a small weighted undirected graph from its edge weights and reports both metric properties and structural properties. It combines shortest-path, spanning-tree, coloring, and traversal checks into one compact graph summary.

It combines Node Count, Source Node, Weight 1-2, Weight 1-3 to estimate Degree Sequence, Connected, Shortest Paths.

Formula & Method

Core equations: Shortest-path relaxation uses

d(v)=\min\left(d(v),d(u)+w_{uv}\right)

, MST growth adds the lightest crossing edge

w(T)=\sum_{e\in T}w_e

, and coloring seeks the minimum

\chi(G)

such that adjacent vertices receive different colors.

Notation used in the formulas: $R$ = Degree Sequence; $x_{1}$ = Node Count; $x_{2}$ = Source Node; $x_{3}$ = Weight 1-2; $x_{4}$ = Weight 1-3; $x_{5}$ = Weight 1-4; $x_{6}$ = Weight 1-5.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you want to inspect a small graph quickly without moving into a full graph library, especially for homework, design sketches, and algorithm sanity checks.

Inputs Used

Node Count: Used directly in the calculation.
Source Node: Used directly in the calculation.
Weight 1-2: 0 means no edge
Weight 1-3: 0 means no edge
Weight 1-4: 0 means no edge
Weight 1-5: 0 means no edge
Weight 2-3: 0 means no edge
Weight 2-4: 0 means no edge
Weight 2-5: 0 means no edge
Weight 3-4: 0 means no edge
Weight 3-5: 0 means no edge
Weight 4-5: 0 means no edge

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