102 lines
3.3 KiB
Python
102 lines
3.3 KiB
Python
|
from itertools import combinations
|
||
|
|
|
||
|
|
__all__ = ["dispersion"]
|
||
|
|
|
||
|
|
|
||
|
|
def dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0):
|
||
|
|
r"""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
|
||
|
|
----------
|
||
|
|
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).
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
def _dispersion(G_u, u, v):
|
||
|
|
"""dispersion for all nodes 'v' in a ego network G_u of node 'u'"""
|
||
|
|
u_nbrs = set(G_u[u])
|
||
|
|
ST = {n for n in G_u[v] if n in u_nbrs}
|
||
|
|
set_uv = {u, v}
|
||
|
|
# all possible ties of connections that u and b share
|
||
|
|
possib = combinations(ST, 2)
|
||
|
|
total = 0
|
||
|
|
for (s, t) in possib:
|
||
|
|
# neighbors of s that are in G_u, not including u and v
|
||
|
|
nbrs_s = u_nbrs.intersection(G_u[s]) - set_uv
|
||
|
|
# s and t are not directly connected
|
||
|
|
if t not in nbrs_s:
|
||
|
|
# s and t do not share a connection
|
||
|
|
if nbrs_s.isdisjoint(G_u[t]):
|
||
|
|
# tick for disp(u, v)
|
||
|
|
total += 1
|
||
|
|
# neighbors that u and v share
|
||
|
|
embededness = len(ST)
|
||
|
|
|
||
|
|
if normalized:
|
||
|
|
if embededness + c != 0:
|
||
|
|
norm_disp = ((total + b) ** alpha) / (embededness + c)
|
||
|
|
else:
|
||
|
|
norm_disp = (total + b) ** alpha
|
||
|
|
dispersion = norm_disp
|
||
|
|
|
||
|
|
else:
|
||
|
|
dispersion = total
|
||
|
|
|
||
|
|
return dispersion
|
||
|
|
|
||
|
|
if u is None:
|
||
|
|
# v and u are not specified
|
||
|
|
if v is None:
|
||
|
|
results = {n: {} for n in G}
|
||
|
|
for u in G:
|
||
|
|
for v in G[u]:
|
||
|
|
results[u][v] = _dispersion(G, u, v)
|
||
|
|
# u is not specified, but v is
|
||
|
|
else:
|
||
|
|
results = dict.fromkeys(G[v], {})
|
||
|
|
for u in G[v]:
|
||
|
|
results[u] = _dispersion(G, v, u)
|
||
|
|
else:
|
||
|
|
# u is specified with no target v
|
||
|
|
if v is None:
|
||
|
|
results = dict.fromkeys(G[u], {})
|
||
|
|
for v in G[u]:
|
||
|
|
results[v] = _dispersion(G, u, v)
|
||
|
|
# both u and v are specified
|
||
|
|
else:
|
||
|
|
results = _dispersion(G, u, v)
|
||
|
|
|
||
|
|
return results
|