U ª9%eã@s ddlmZdgZddd„ZdS) é)ÚcombinationsÚ dispersionNTçð?çc sÖ‡‡‡‡fdd„}|dkrŽ|dkr^dd„|Dƒ}|D]&}||D]}||||ƒ|||<q@q4qÒt ||i¡}||D]}||||ƒ||<qvnD|dkrÆt ||i¡}||D]}||||ƒ||<q®n||||ƒ}|S)aœCalculate 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 ---------- G : graph A NetworkX graph. u : node, optional The source for the dispersion score (e.g. ego node of the network). v : node, optional The target of the dispersion score if specified. normalized : bool If True (default) normalize by the embededness of the nodes (u and v). alpha, b, c : float 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 ------- nodes : dictionary 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 :func:`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 cs®t||ƒ‰‡fdd„||Dƒ}||h}t|dƒ}d}|D]8\}}ˆ ||¡|} || kr<| ||¡r<|d7}q9sz2dispersion.._dispersion..éré)ÚsetrÚintersectionÚ isdisjointÚlen)ZG_uÚuÚvZSTZset_uvZpossibÚtotalÚsÚtZnbrs_sZembedednessZdispersion_val©ÚalphaÚbÚcÚ normalizedr rÚ_dispersion6s" zdispersion.._dispersionNcSsi|] }|i“qSrrrrrrÚ Uszdispersion..)ÚdictÚfromkeys) ÚGrrrrrrrÚresultsrrrrs 0)NNTrrr)Ú itertoolsrÚ__all__rrrrrÚs