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partition_quality(G, partition)

The coverage of a partition is the ratio of the number of intra-community edges to the total number of edges in the graph.

The performance of a partition is the number of intra-community edges plus inter-community non-edges divided by the total number of potential edges.

This algorithm has complexity $O(C^2 + L)$ where C is the number of communities and L is the number of links.

Notes

If G is a multigraph;

  • for coverage, the multiplicity of edges is counted

  • for performance, the result is -1 (total number of possible edges is not defined)

Parameters

G : NetworkX graph
partition : sequence

Partition of the nodes of G, represented as a sequence of sets of nodes (blocks). Each block of the partition represents a community.

Raises

NetworkXError

If :None:None:`partition` is not a valid partition of the nodes of G.

Returns

(float, float)

The (coverage, performance) tuple of the partition, as defined above.

Returns the coverage and performance of a partition of G.

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /networkx/algorithms/community/quality.py#356
type: <class 'function'>
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