"""
Label propagation community detection algorithms.
"""
from collections import Counter, defaultdict, deque
import networkx as nx
from networkx.utils import groups, not_implemented_for, py_random_state
__all__ = [
"label_propagation_communities",
"asyn_lpa_communities",
"fast_label_propagation_communities",
]
[docs]
@py_random_state("seed")
@nx._dispatchable(edge_attrs="weight")
def fast_label_propagation_communities(G, *, weight=None, seed=None):
"""Returns communities in `G` as detected by fast label propagation.
The fast label propagation algorithm is described in [1]_. The algorithm is
probabilistic and the found communities may vary in different executions.
The algorithm operates as follows. First, the community label of each node is
set to a unique label. The algorithm then repeatedly updates the labels of
the nodes to the most frequent label in their neighborhood. In case of ties,
a random label is chosen from the most frequent labels.
The algorithm maintains a queue of nodes that still need to be processed.
Initially, all nodes are added to the queue in a random order. Then the nodes
are removed from the queue one by one and processed. If a node updates its label,
all its neighbors that have a different label are added to the queue (if not
already in the queue). The algorithm stops when the queue is empty.
Parameters
----------
G : Graph, DiGraph, MultiGraph, or MultiDiGraph
Any NetworkX graph.
weight : string, or None (default)
The edge attribute representing a non-negative weight of an edge. If None,
each edge is assumed to have weight one. The weight of an edge is used in
determining the frequency with which a label appears among the neighbors of
a node (edge with weight `w` is equivalent to `w` unweighted edges).
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
-----
Edge directions are ignored for directed graphs.
Edge weights must be non-negative numbers.
References
----------
.. [1] Vincent A. Traag & Lovro Šubelj. "Large network community detection by
fast label propagation." Scientific Reports 13 (2023): 2701.
https://doi.org/10.1038/s41598-023-29610-z
"""
# Queue of nodes to be processed.
nodes_queue = deque(G)
seed.shuffle(nodes_queue)
# Set of nodes in the queue.
nodes_set = set(G)
# Assign unique label to each node.
comms = {node: i for i, node in enumerate(G)}
while nodes_queue:
# Remove next node from the queue to process.
node = nodes_queue.popleft()
nodes_set.remove(node)
# Isolated nodes retain their initial label.
if G.degree(node) > 0:
# Compute frequency of labels in node's neighborhood.
label_freqs = _fast_label_count(G, comms, node, weight)
max_freq = max(label_freqs.values())
# Always sample new label from most frequent labels.
comm = seed.choice(
[comm for comm in label_freqs if label_freqs[comm] == max_freq]
)
if comms[node] != comm:
comms[node] = comm
# Add neighbors that have different label to the queue.
for nbr in nx.all_neighbors(G, node):
if comms[nbr] != comm and nbr not in nodes_set:
nodes_queue.append(nbr)
nodes_set.add(nbr)
yield from groups(comms).values()
def _fast_label_count(G, comms, node, weight=None):
"""Computes the frequency of labels in the neighborhood of a node.
Returns a dictionary keyed by label to the frequency of that label.
"""
if weight is None:
# Unweighted (un)directed simple graph.
if not G.is_multigraph():
label_freqs = Counter(map(comms.get, nx.all_neighbors(G, node)))
# Unweighted (un)directed multigraph.
else:
label_freqs = defaultdict(int)
for nbr in G[node]:
label_freqs[comms[nbr]] += len(G[node][nbr])
if G.is_directed():
for nbr in G.pred[node]:
label_freqs[comms[nbr]] += len(G.pred[node][nbr])
else:
# Weighted undirected simple/multigraph.
label_freqs = defaultdict(float)
for _, nbr, w in G.edges(node, data=weight, default=1):
label_freqs[comms[nbr]] += w
# Weighted directed simple/multigraph.
if G.is_directed():
for nbr, _, w in G.in_edges(node, data=weight, default=1):
label_freqs[comms[nbr]] += w
return label_freqs
[docs]
@py_random_state(2)
@nx._dispatchable(edge_attrs="weight")
def asyn_lpa_communities(G, weight=None, seed=None):
"""Returns communities in `G` as detected by asynchronous label
propagation.
The asynchronous label propagation algorithm is described in
[1]_. The algorithm is probabilistic and the found communities may
vary on different executions.
The algorithm proceeds as follows. After initializing each node with
a unique label, the algorithm repeatedly sets the label of a node to
be the label that appears most frequently among that nodes
neighbors. The algorithm halts when each node has the label that
appears most frequently among its neighbors. The algorithm is
asynchronous because each node is updated without waiting for
updates on the remaining nodes.
This generalized version of the algorithm in [1]_ accepts edge
weights.
Parameters
----------
G : Graph
weight : string
The edge attribute representing the weight of an edge.
If None, each edge is assumed to have weight one. In this
algorithm, the weight of an edge is used in determining the
frequency with which a label appears among the neighbors of a
node: a higher weight means the label appears more often.
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
-----
Edge weight attributes must be numerical.
References
----------
.. [1] Raghavan, Usha Nandini, Réka Albert, and Soundar Kumara. "Near
linear time algorithm to detect community structures in large-scale
networks." Physical Review E 76.3 (2007): 036106.
"""
labels = {n: i for i, n in enumerate(G)}
cont = True
while cont:
cont = False
nodes = list(G)
seed.shuffle(nodes)
for node in nodes:
if not G[node]:
continue
# Get label frequencies among adjacent nodes.
# Depending on the order they are processed in,
# some nodes will be in iteration t and others in t-1,
# making the algorithm asynchronous.
if weight is None:
# initialising a Counter from an iterator of labels is
# faster for getting unweighted label frequencies
label_freq = Counter(map(labels.get, G[node]))
else:
# updating a defaultdict is substantially faster
# for getting weighted label frequencies
label_freq = defaultdict(float)
for _, v, wt in G.edges(node, data=weight, default=1):
label_freq[labels[v]] += wt
# Get the labels that appear with maximum frequency.
max_freq = max(label_freq.values())
best_labels = [
label for label, freq in label_freq.items() if freq == max_freq
]
# If the node does not have one of the maximum frequency labels,
# randomly choose one of them and update the node's label.
# Continue the iteration as long as at least one node
# doesn't have a maximum frequency label.
if labels[node] not in best_labels:
labels[node] = seed.choice(best_labels)
cont = True
yield from groups(labels).values()
[docs]
@not_implemented_for("directed")
@nx._dispatchable
def label_propagation_communities(G):
"""Generates community sets determined by label propagation
Finds communities in `G` using a semi-synchronous label propagation
method [1]_. This method combines the advantages of both the synchronous
and asynchronous models. Not implemented for directed graphs.
Parameters
----------
G : graph
An undirected NetworkX graph.
Returns
-------
communities : iterable
A dict_values object that contains a set of nodes for each community.
Raises
------
NetworkXNotImplemented
If the graph is directed
References
----------
.. [1] Cordasco, G., & Gargano, L. (2010, December). Community detection
via semi-synchronous label propagation algorithms. In Business
Applications of Social Network Analysis (BASNA), 2010 IEEE International
Workshop on (pp. 1-8). IEEE.
"""
coloring = _color_network(G)
# Create a unique label for each node in the graph
labeling = {v: k for k, v in enumerate(G)}
while not _labeling_complete(labeling, G):
# Update the labels of every node with the same color.
for color, nodes in coloring.items():
for n in nodes:
_update_label(n, labeling, G)
clusters = defaultdict(set)
for node, label in labeling.items():
clusters[label].add(node)
return clusters.values()
def _color_network(G):
"""Colors the network so that neighboring nodes all have distinct colors.
Returns a dict keyed by color to a set of nodes with that color.
"""
coloring = {} # color => set(node)
colors = nx.coloring.greedy_color(G)
for node, color in colors.items():
if color in coloring:
coloring[color].add(node)
else:
coloring[color] = {node}
return coloring
def _labeling_complete(labeling, G):
"""Determines whether or not LPA is done.
Label propagation is complete when all nodes have a label that is
in the set of highest frequency labels amongst its neighbors.
Nodes with no neighbors are considered complete.
"""
return all(
labeling[v] in _most_frequent_labels(v, labeling, G) for v in G if len(G[v]) > 0
)
def _most_frequent_labels(node, labeling, G):
"""Returns a set of all labels with maximum frequency in `labeling`.
Input `labeling` should be a dict keyed by node to labels.
"""
if not G[node]:
# Nodes with no neighbors are themselves a community and are labeled
# accordingly, hence the immediate if statement.
return {labeling[node]}
# Compute the frequencies of all neighbors of node
freqs = Counter(labeling[q] for q in G[node])
max_freq = max(freqs.values())
return {label for label, freq in freqs.items() if freq == max_freq}
def _update_label(node, labeling, G):
"""Updates the label of a node using the Prec-Max tie breaking algorithm
The algorithm is explained in: 'Community Detection via Semi-Synchronous
Label Propagation Algorithms' Cordasco and Gargano, 2011
"""
high_labels = _most_frequent_labels(node, labeling, G)
if len(high_labels) == 1:
labeling[node] = high_labels.pop()
elif len(high_labels) > 1:
# Prec-Max
if labeling[node] not in high_labels:
labeling[node] = max(high_labels)
