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Calcimator

Graph Theory Calculator

Analyze graph properties including degree, density, connectivity, and Eulerian path possibility.

Inputs

Results

Average Degree

2.33

Graph Density0.4667
Possibly ConnectedYes
Max Possible Degree5
Eulerian Circuit PossibleNot possible
Max Possible Edges15
How to Use This Calculator
  1. Enter the number of Vertices (V) and Edges (E) in the graph.
  2. Set Directed to 1 if the graph is a directed graph (digraph), or 0 for undirected.
  3. Review Average Degree — for undirected graphs this equals 2E/V by the handshaking lemma.
  4. Check Graph Density — values near 0 indicate sparse graphs, near 1 indicate dense graphs.
  5. Use Max Edges to determine how close the graph is to being complete.

How the result changes with Vertices (V)

Vertices (V)Average Degree
1010.14
3510.04
6500.02
9000.02

What each input means

Vertices (V)
Number of vertices (nodes) in the graph
Edges (E)
Number of edges (connections) in the graph
Directed (0=No, 1=Yes)
Whether the graph is directed (digraph) or undirected

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Vertices (V) = 6, Edges (E) = 7, Directed (0=No, 1=Yes) = 0 = 3 input(s) provided
  2. Calculate Average Degree
    Average Degree
    2.33 = 2.33
  3. Calculate Graph Density
    Graph Density
    0.4667 = 0.4667
  4. Calculate Possibly Connected
    Possibly Connected
    Yes = Yes

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators.

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