dispersion

dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0)

Calculate dispersion between u and v in G.

A link between two actors (u and v) has a high dispersion when their mutual ties (s and t) are not well connected with each other.

Parameters:

Ggraph

A NetworkX graph.

unode, optional

The source for the dispersion score (e.g. ego node of the network).

vnode, optional

The target of the dispersion score if specified.

normalizedbool

If True (default) normalize by the embeddedness of the nodes (u and v).

alpha, b, cfloat

Parameters for the normalization procedure. When normalized is True, the dispersion value is normalized by:

result = ((dispersion + b) ** alpha) / (embeddedness + c)

as long as the denominator is nonzero.

Returns:

nodesdictionary

If u (v) is specified, returns a dictionary of nodes with dispersion score for all “target” (“source”) nodes. If neither u nor v is specified, returns a dictionary of dictionaries for all nodes ‘u’ in the graph with a dispersion score for each node ‘v’.

Notes

This implementation follows Lars Backstrom and Jon Kleinberg [1]. Typical usage would be to run dispersion on the ego network \(G_u\) if \(u\) were specified. Running dispersion() with neither \(u\) nor \(v\) specified can take some time to complete.

References

[1]

Romantic Partnerships and the Dispersion of Social Ties: A Network Analysis of Relationship Status on Facebook. Lars Backstrom, Jon Kleinberg. https://arxiv.org/pdf/1310.6753v1.pdf