LFR_benchmark_graph(n, tau1, tau2, mu, average_degree=None, min_degree=None, max_degree=None, min_community=None, max_community=None, tol=1e-07, max_iters=500, seed=None)
This algorithm proceeds as follows:
Find a degree sequence with a power law distribution, and minimum value min_degree
, which has approximate average degree average_degree
. This is accomplished by either
specifying min_degree
and not average_degree
,
specifying average_degree
and not min_degree
, in which case a suitable minimum degree will be found.
max_degree
can also be specified, otherwise it will be set to n
. Each node u will have :None:None:`\mu \mathrm{deg}(u)` edges joining it to nodes in communities other than its own and :None:None:`(1 -
\mu) \mathrm{deg}(u)` edges joining it to nodes in its own community.
Generate community sizes according to a power law distribution with exponent tau2
. If min_community
and max_community
are not specified they will be selected to be min_degree
and max_degree
, respectively. Community sizes are generated until the sum of their sizes equals n
.
Each node will be randomly assigned a community with the condition that the community is large enough for the node's intra-community degree, :None:None:`(1 - \mu) \mathrm{deg}(u)` as described in step 2. If a community grows too large, a random node will be selected for reassignment to a new community, until all nodes have been assigned a community.
Each node u then adds :None:None:`(1 - \mu) \mathrm{deg}(u)` intra-community edges and :None:None:`\mu \mathrm{deg}(u)` inter-community edges.
This algorithm differs slightly from the original way it was presented in [1].
Rather than connecting the graph via a configuration model then rewiring to match the intra-community and inter-community degrees, we do this wiring explicitly at the end, which should be equivalent.
The code posted on the author's website [2] calculates the random power law distributed variables and their average using continuous approximations, whereas we use the discrete distributions here as both degree and community size are discrete.
Though the authors describe the algorithm as quite robust, testing during development indicates that a somewhat narrower parameter set is likely to successfully produce a graph. Some suggestions have been provided in the event of exceptions.
Number of nodes in the created graph.
Power law exponent for the degree distribution of the created graph. This value must be strictly greater than one.
Power law exponent for the community size distribution in the created graph. This value must be strictly greater than one.
Fraction of inter-community edges incident to each node. This value must be in the interval [0, 1].
Desired average degree of nodes in the created graph. This value must be in the interval [0, n]. Exactly one of this and min_degree
must be specified, otherwise a NetworkXError
is raised.
Minimum degree of nodes in the created graph. This value must be in the interval [0, n]. Exactly one of this and average_degree
must be specified, otherwise a NetworkXError
is raised.
Maximum degree of nodes in the created graph. If not specified, this is set to n
, the total number of nodes in the graph.
Minimum size of communities in the graph. If not specified, this is set to min_degree
.
Maximum size of communities in the graph. If not specified, this is set to n
, the total number of nodes in the graph.
Tolerance when comparing floats, specifically when comparing average degree values.
Maximum number of iterations to try to create the community sizes, degree distribution, and community affiliations.
Indicator of random number generation state. See Randomness<randomness>
.
If any of the parameters do not meet their upper and lower bounds:
tau1
and tau2
must be strictly greater than 1.
mu
must be in [0, 1].
max_degree
must be in {1, ..., n}.
min_community
and max_community
must be in {0, ..., n}.
If not exactly one of average_degree
and min_degree
is specified.
If min_degree
is not specified and a suitable min_degree
cannot be found.
If a valid degree sequence cannot be created within max_iters
number of iterations.
If a valid set of community sizes cannot be created within max_iters
number of iterations.
If a valid community assignment cannot be created within 10 *
n * max_iters
number of iterations.
The LFR benchmark graph generated according to the specified parameters.
Each node in the graph has a node attribute 'community'
that stores the community (that is, the set of nodes) that includes it.
Returns the LFR benchmark graph.
>>> from networkx.generators.community import LFR_benchmark_graph >>> n = 250 >>> tau1 = 3 >>> tau2 = 1.5 >>> mu = 0.1 >>> G = LFR_benchmark_graph( ... n, tau1, tau2, mu, average_degree=5, min_community=20, seed=10 ... )
>>> communities = {frozenset(G.nodes[v]["community"]) for v in G}Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them