106 lines
3.5 KiB
Python
106 lines
3.5 KiB
Python
from itertools import combinations
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__author__ = "\n".join(['Ben Edwards (bedwards@cs.unm.edu)',
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'Huston Hedinger (hstn@hdngr.com)',
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'Dan Schult (dschult@colgate.edu)'])
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__all__ = ['dispersion']
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def dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0):
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r"""Calculate dispersion between `u` and `v` in `G`.
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A link between two actors (`u` and `v`) has a high dispersion when their
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mutual ties (`s` and `t`) are not well connected with each other.
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Parameters
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----------
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G : graph
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A NetworkX graph.
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u : node, optional
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The source for the dispersion score (e.g. ego node of the network).
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v : node, optional
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The target of the dispersion score if specified.
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normalized : bool
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If True (default) normalize by the embededness of the nodes (u and v).
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Returns
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-------
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nodes : dictionary
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If u (v) is specified, returns a dictionary of nodes with dispersion
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score for all "target" ("source") nodes. If neither u nor v is
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specified, returns a dictionary of dictionaries for all nodes 'u' in the
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graph with a dispersion score for each node 'v'.
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Notes
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-----
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This implementation follows Lars Backstrom and Jon Kleinberg [1]_. Typical
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usage would be to run dispersion on the ego network $G_u$ if $u$ were
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specified. Running :func:`dispersion` with neither $u$ nor $v$ specified
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can take some time to complete.
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References
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----------
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.. [1] Romantic Partnerships and the Dispersion of Social Ties:
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A Network Analysis of Relationship Status on Facebook.
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Lars Backstrom, Jon Kleinberg.
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https://arxiv.org/pdf/1310.6753v1.pdf
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"""
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def _dispersion(G_u, u, v):
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"""dispersion for all nodes 'v' in a ego network G_u of node 'u'"""
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u_nbrs = set(G_u[u])
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ST = set(n for n in G_u[v] if n in u_nbrs)
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set_uv = set([u, v])
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# all possible ties of connections that u and b share
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possib = combinations(ST, 2)
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total = 0
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for (s, t) in possib:
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# neighbors of s that are in G_u, not including u and v
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nbrs_s = u_nbrs.intersection(G_u[s]) - set_uv
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# s and t are not directly connected
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if t not in nbrs_s:
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# s and t do not share a connection
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if nbrs_s.isdisjoint(G_u[t]):
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# tick for disp(u, v)
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total += 1
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# neighbors that u and v share
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embededness = len(ST)
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if normalized:
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if embededness + c != 0:
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norm_disp = ((total + b)**alpha) / (embededness + c)
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else:
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norm_disp = (total + b)**alpha
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dispersion = norm_disp
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else:
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dispersion = total
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return dispersion
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if u is None:
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# v and u are not specified
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if v is None:
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results = dict((n, {}) for n in G)
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for u in G:
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for v in G[u]:
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results[u][v] = _dispersion(G, u, v)
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# u is not specified, but v is
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else:
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results = dict.fromkeys(G[v], {})
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for u in G[v]:
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results[u] = _dispersion(G, v, u)
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else:
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# u is specified with no target v
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if v is None:
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results = dict.fromkeys(G[u], {})
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for v in G[u]:
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results[v] = _dispersion(G, u, v)
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# both u and v are specified
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else:
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results = _dispersion(G, u, v)
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return results
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