a h+@s.ddlmZddlZdgZejdddZdS) ) combinationsN dispersionT?c sfdd}|dur|dur^dd|D}|D]&}||D]}|||||||<q@q4qt||i}||D]}||||||<qvnD|durt||i}||D]}||||||<qn ||||}|S)aCalculate 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 embeddedness 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 c st||fdd||D}||h}t|d}d}|D]8\}}|||} || vr<| ||r<|d7}q<z2dispersion.._dispersion..r)setr intersection isdisjointlen) ZG_uuvZSTZset_uvZpossibtotalstZnbrs_sZ embeddednessZdispersion_valalphabc normalizedr r _dispersion9s"       zdispersion.._dispersionNcSsi|] }|iqSrrrrrr Xr zdispersion..)dictfromkeys) Grrrrrrrresultsrrr rs 1    )NNTrrr) itertoolsrZnetworkxZnx__all__ _dispatchrrrrr s