# localModularity: Algorithms using local modularity In modMax: Community Structure Detection via Modularity Maximization

## Description

`localModularity` uses the local modularity to identify the local community structure around a certain vertex

`localModularityWang` uses the local modularity to identify the community structure of the entire network

## Usage

 ```1 2``` ```localModularity(adjacency, srcV, k) localModularityWang(adjacency,numRandom=0) ```

## Arguments

 `adjacency` A nonnegative symmetric adjacency matrix of the network whose community structur will be analyzed `srcV` A given vertex whose local community structure should be determined by `localModularity` `k` The maximum number of vertices to add to the local community of `srcV` `numRandom` The number of random networks with which the modularity of the resulting community structure should be compared (default: no comparison). see details below for further explanation of the used null model.

## Details

The used random networks have the same number of vertices and the same degree distribution as the original network.

## Value

The result for `localModularity` is returned as a list with the following components

 `local community structure` Vertices assigned to the same community as the source vertex `srcV` `local modularity` The local modularity value for the determined local community

The result for `localModularityWang` is returned as a list with the following components

 `number of communities` The number of communities detected by the algorithm `modularity` The modularity of the detected community structure `mean` The mean of the modularity values for random networks, only computed if `numRandom>0` `standard deviation` The standard deviation of the modularity values for random networks, only computed if `numRandom>0` `community structure` The community structure of the examined network given by a vector assigning each vertex its community number `random modularity values` The list of the modularity values for random networks, only computed if `numRandom>0`

## Author(s)

Maria Schelling, Cang Hui

## References

Clauset, A. Finding local community structure in networks. Phys. Rev. E, 72:026132, Aug 2005.

Wang, X., Chen, G. and Lu, H. A very fast algorithm for detecting community structures in complex networks. Physica A: Statistical Mechanics and its Applications, 384(2):667-674, 2007.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```#unweighted network randomgraph1 <- erdos.renyi.game(10, 0.3, type="gnp",directed = FALSE, loops = FALSE) #to ensure that the graph is connected vertices1 <- which(clusters(randomgraph1)\$membership==1) graph1 <- induced.subgraph(randomgraph1,vertices1) adj1 <- get.adjacency(graph1) result1 <- localModularity(adj1, srcV=1, k=4) #weighted network randomgraph2 <- erdos.renyi.game(10, 0.3, type="gnp",directed = FALSE, loops = FALSE) #to ensure that the graph is connected vertices2 <- which(clusters(randomgraph2)\$membership==1) graph2 <- induced.subgraph(randomgraph2,vertices2) graph2 <- set.edge.attribute(graph2, "weight", value=runif(ecount(graph2),0,1)) adj2 <- get.adjacency(graph2, attr="weight") result2 <- localModularityWang(adj2) ```

### Example output

```Loading required package: gtools

Attaching package: 'igraph'

The following object is masked from 'package:gtools':

permute

The following objects are masked from 'package:stats':

decompose, spectrum

The following object is masked from 'package:base':

union
```

modMax documentation built on May 2, 2019, 12:20 p.m.