spinglass.community {igraph}R Documentation

Finding communities in graphs based on statistical meachanics

Description

This function tries to find communities in graphs via a spin-glass model and simulated annealing.

Usage

spinglass.community(graph, weights=NULL, spins=25, parupdate=FALSE,
                    start.temp=1, stop.temp=0.1, cool.fact=0.99,
                    update.rule=c("config", "random", "simple"), gamma=1)
spinglass.community(graph, weights=NULL, vertex, spins=25,
                    update.rule=c("config", "random", "simple"), gamma=1)

Arguments

graph The input graph, can be directed but the direction of the edges is neglected.
weights The weights of the edges. Either a numeric vector or NULL. If it is null and the input graph has a ‘weight’ edge attribute then that will be used. If NULL and no such attribute is present then the edges will have equal weights.
spins Integer constant, the number of spins to use. This is the upper limit for the number of communities. It is not a problem to supply a (reasonably) big number here, in which case some spin states will be unpopulated.
parupdate Logical constant, whether to update the spins of the vertices in parallel (synchronously) or not. This argument is ignored if the second form of the function is used (ie. the ‘vertex’ argument is present).
start.temp Real constant, the start temperature. This argument is ignored if the second form of the function is used (ie. the ‘vertex’ argument is present).
stop.temp Real constant, the stop temperature. The simulation terminates if the temperature lowers below this level. This argument is ignored if the second form of the function is used (ie. the ‘vertex’ argument is present).
cool.fact Cooling factor for the simulated annealing. This argument is ignored if the second form of the function is used (ie. the ‘vertex’ argument is present).
update.rule Character constant giving the ‘null-model’ of the simulation. Possible values: “simple” and “config”. “simple” uses a random graph with the same number of edges as the baseline probability and “config” uses a random graph with the same vertex degrees as the input graph.
gamma Real constant, the gamma argument of the algorithm. This specifies the balance between the importance of present and non-present edges in a community. Roughly, a comunity is a set of vertices having many edges inside the community and few edges outside the community. The default 1.0 value makes existing and non-existing links equally important. Smaller values make the existing links, greater values the missing links more important.
vertex This parameter can be used to calculate the community of a given vertex without calculating all communities. Note that if this argument is present then some other arguments are ignored.

Details

This function tries to find communities in a graph. A community is a set of nodes with many edges inside the community and few edges between outside it (ie. between the community itself and the rest of the graph.

Value

If the vertex argument is not given, ie. the first form is used then a named list is returned with the following slots:

membership Integer vector giving the communities found. The communities have ids starting from zero and for each graph vertex ids community id is given in this vector.
csize The sizes of the communities in the order of their ids.
modularity The modularity score of the result, as defined by Newman and Girvan, see references.
temperature The temperature of the system when the algorithm terminated.
community Numeric vector giving the ids of the vertices in the same community as vertex.
cohesion The cohesion score of the result, see references.
adhesion The adhesion score of the result, see references.
inner.links The number of edges within the community of vertex.
outer.links The number of edges between the community of vertex and the rest of the graph.

Author(s)

Jorg Reichardt lastname@physik.uni-wuerzburg.de for the original code and Gabor Csardi csardi@rmki.kfki.hu for the igraph glue code

References

J. Reichardt and S. Bornholdt: Statistical Mechanics of Community Detection, Phys. Rev. E, 74, 016110 (2006), http://arxiv.org/abs/cond-mat/0603718

M. E. J. Newman and M. Girvan: Finding and evaluating community structure in networks, Phys. Rev. E 69, 026113 (2004)

See Also

clusters

Examples

  g <- erdos.renyi.game(10, 5/10) %du% erdos.renyi.game(9, 5/9)
  g <- add.edges(g, c(0, 11))
  g <- subgraph(g, subcomponent(g, 0))
  spinglass.community(g, spins=2)
  spinglass.community(g, vertex=0)

[Package igraph version 0.5.2 Index]