# spinglass.community

0th

Percentile

##### Finding communities in graphs based on statistical meachanics

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

Keywords
graphs
##### 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
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 presen
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 probab
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 edge
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:
• membershipInteger 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.
• csizeThe sizes of the communities in the order of their ids.
• modularityThe modularity score of the result, as defined by Newman and Girvan, see references.
• temperatureThe temperature of the system when the algorithm terminated.
• If the vertex argument is present, ie. the second form is used then a named list is returned with the following components:
• communityNumeric vector giving the ids of the vertices in the same community as vertex.
• cohesionThe cohesion score of the result, see references.
• inner.linksThe number of edges within the community of vertex.
• outer.linksThe number of edges between the community of vertex and the rest of the graph.

##### concept

• Statistical mechanics
• Spin-glass
• Community structure

##### synopsis

spinglass.community(graph, weights=NULL, vertex=NULL, spins=25, parupdate=FALSE, start.temp=1, stop.temp=0.01, cool.fact=0.99, update.rule=c("config", "random", "simple"), gamma=1)

##### 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)

clusters

##### Aliases
• spinglass.community
##### Examples
g <- erdos.renyi.game(10, 5/10) %du% erdos.renyi.game(9, 5/9)
spinglass.community(g, vertex=0)