# -*- coding: utf-8 -*-
# Copyright (C) 2017-2018
# All rights reserved.
# BSD license.
# Author: Ferran Parés <ferran.pares@bsc.es>
"""Asynchronous Fluid Communities algorithm for community detection."""
from collections import Counter
from networkx.exception import NetworkXError
from networkx.algorithms.components import is_connected
from networkx.utils import groups
from networkx.utils import not_implemented_for
from networkx.utils import py_random_state
__all__ = ['asyn_fluidc']
[docs]@py_random_state(3)
@not_implemented_for('directed', 'multigraph')
def asyn_fluidc(G, k, max_iter=100, seed=None):
"""Returns communities in `G` as detected by Fluid Communities algorithm.
The asynchronous fluid communities algorithm is described in
[1]_. The algorithm is based on the simple idea of fluids interacting
in an environment, expanding and pushing each other. It's initialization is
random, so found communities may vary on different executions.
The algorithm proceeds as follows. First each of the initial k communities
is initialized in a random vertex in the graph. Then the algorithm iterates
over all vertices in a random order, updating the community of each vertex
based on its own community and the communities of its neighbours. This
process is performed several times until convergence.
At all times, each community has a total density of 1, which is equally
distributed among the vertices it contains. If a vertex changes of
community, vertex densities of affected communities are adjusted
immediately. When a complete iteration over all vertices is done, such that
no vertex changes the community it belongs to, the algorithm has converged
and returns.
This is the original version of the algorithm described in [1]_.
Unfortunately, it does not support weighted graphs yet.
Parameters
----------
G : Graph
k : integer
The number of communities to be found.
max_iter : integer
The number of maximum iterations allowed. By default 15.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
communities : iterable
Iterable of communities given as sets of nodes.
Notes
-----
k variable is not an optional argument.
References
----------
.. [1] Parés F., Garcia-Gasulla D. et al. "Fluid Communities: A
Competitive and Highly Scalable Community Detection Algorithm".
[https://arxiv.org/pdf/1703.09307.pdf].
"""
# Initial checks
if not isinstance(k, int):
raise NetworkXError("k must be an integer.")
if not k > 0:
raise NetworkXError("k must be greater than 0.")
if not is_connected(G):
raise NetworkXError("Fluid Communities require connected Graphs.")
if len(G) < k:
raise NetworkXError("k cannot be bigger than the number of nodes.")
# Initialization
max_density = 1.0
vertices = list(G)
seed.shuffle(vertices)
communities = {n: i for i, n in enumerate(vertices[:k])}
density = {}
com_to_numvertices = {}
for vertex in communities.keys():
com_to_numvertices[communities[vertex]] = 1
density[communities[vertex]] = max_density
# Set up control variables and start iterating
iter_count = 0
cont = True
while cont:
cont = False
iter_count += 1
# Loop over all vertices in graph in a random order
vertices = list(G)
seed.shuffle(vertices)
for vertex in vertices:
# Updating rule
com_counter = Counter()
# Take into account self vertex community
try:
com_counter.update({communities[vertex]:
density[communities[vertex]]})
except KeyError:
pass
# Gather neighbour vertex communities
for v in G[vertex]:
try:
com_counter.update({communities[v]:
density[communities[v]]})
except KeyError:
continue
# Check which is the community with highest density
new_com = -1
if len(com_counter.keys()) > 0:
max_freq = max(com_counter.values())
best_communities = [com for com, freq in com_counter.items()
if (max_freq - freq) < 0.0001]
# If actual vertex com in best communities, it is preserved
try:
if communities[vertex] in best_communities:
new_com = communities[vertex]
except KeyError:
pass
# If vertex community changes...
if new_com == -1:
# Set flag of non-convergence
cont = True
# Randomly chose a new community from candidates
new_com = seed.choice(best_communities)
# Update previous community status
try:
com_to_numvertices[communities[vertex]] -= 1
density[communities[vertex]] = max_density / \
com_to_numvertices[communities[vertex]]
except KeyError:
pass
# Update new community status
communities[vertex] = new_com
com_to_numvertices[communities[vertex]] += 1
density[communities[vertex]] = max_density / \
com_to_numvertices[communities[vertex]]
# If maximum iterations reached --> output actual results
if iter_count > max_iter:
break
# Return results by grouping communities as list of vertices
return iter(groups(communities).values())