[BUG] Eigenvector centrality for disconnected graphs

[greimel]

Description of bug

In a disconnected graph, eigenvector_centrality sometimes delivers random results.

g = SimpleGraph(6)
add_edge!.(Ref(g), 1:3, (1:3)')
add_edge!.(Ref(g), 4:6, (4:6)')

eigenvector_centrality(g)

Run this multiple times, the numbers are always different.

Strictly speaking,

Eigenvector centrality is not well-defined for disconnected graphs since the centrality scores of the individual components are independent of each other

source on stackoverflow

Here's what Matlab does

[...] If there are several disconnected components, then the algorithm computes the eigenvector centrality individually for each component, then scales the scores according to the percentage of graph nodes in that component. The centrality score of disconnected nodes is 1/numnodes(G).

https://de.mathworks.com/help/matlab/ref/graph.centrality.html

Potential fixes

• add a warning to the documentation
• check if a graph is connected and warn/error if it isn't
• emulate Matlab's behavior

[gdalle]

Hi, thanks for catching this! Which fix would you feel like implementing?