spectral_igraph_membership {rSpectral}

Spectral clustering for igraph objects

Description

This function implements the network clustering algorithm described in (M. E. J. Newman, 2006).

Usage

spectral_igraph_membership(
  g,
  Cn_min = 1L,
  tol = 1e-05,
  names = 1L,
  fix_neig = 0L
)

Arguments

g

igraph object

Cn_min

minimum cluster size

tol

tolerance

names

are we dealing with alphaNumeric (1) or numeric (!1) ids

fix_neig

whether to fix neighbouring nodes found in same community

Details

The complete iterative algorithm comprises of two steps. In the first step, the network is expressed in terms of its leading eigenvalue and eigenvector and recursively partition into two communities. Partitioning occurs if the maximum positive eigenvalue is greater than the tolerance (tol=10-5) for the current partition, and if it results in a positive contribution to the Modularity.

Given an initial separation using the leading eigen step, the function then continues to maximise for the change in Modularity using a fine-tuning step - or variate thereof. The first stage here is to find the node which, when moved from one community to another, gives the maximum change in Modularity. This node’s community is then fixed and we repeat the process until all nodes have been moved. The whole process is repeated from this new state until the change in the Modularity, between the new and old state, is less than the predefined tolerance (tol).

A slight variant of the fine-tuning step, which can reduce execution time by factor 2 to 5, is also provided. Instead of moving each node into each community in turn, we only consider moves of neighbouring nodes, found in different communities, to the community of the current node of interest. This variant of the node-moving algorithm effectively 'fixes' neigbouring nodes fix_neig in the community being considered.

The two steps process is repeatedly applied to each new community found, subdivided each community into two new communities, until we are unable to find any division that results in a positive change in Modularity. An additional stopping criteria, based on the minimum cluster size Cn_min, is also provided.

Value

data.frame with node names and membership information

Examples

data(karate,package='igraphdata')
df.mem<-spectral_igraph_membership(karate)