# spinglass.community

##### 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 aweight 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
argument is present).`vertex`

- start.temp
- Real constant, the start temperature.
This argument is ignored if the second form of the
function is used (ie. the
argument is present).`vertex`

- 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
argument is presen`vertex`

- cool.fact
- Cooling factor for the simulated annealing.
This argument is ignored if the second form of the
function is used (ie. the
argument is present).`vertex`

- update.rule
- Character constant giving the
null-model of the simulation. Possible values:simple andconfig .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: 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. - If the
`vertex`

argument is present, ie. the second form is used then a named list is returned with the following components: 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.

##### 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),

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

##### See Also

##### 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)
```

*Documentation reproduced from package igraph, version 0.5.3, License: GPL (>= 2)*