## S3 method for class 'igraph':
modularity(x, membership, weights = NULL, ...)modularity_matrix(graph, membership, weights = NULL)
NULL then a numeric vector giving edge weights.modularity a numeric scalar, the modularity score of the
given configuration.For modularity_matrix a numeic square matrix, its order is the number of
vertices in the graph.
modularity calculates the modularity of a graph with respect to the
given membership vector.The modularity of a graph with respect to some division (or vertex types) measures how good the division is, or how separated are the different vertex types from each other. It defined as $$Q=\frac{1}{2m} \sum_{i,j} (A_{ij}-\frac{k_ik_j}{2m})\delta(c_i,c_j),$$ here $m$ is the number of edges, $A_{ij}$ is the element of the $A$ adjacency matrix in row $i$ and column $j$, $k_i$ is the degree of $i$, $k_j$ is the degree of $j$, $c_i$ is the type (or component) of $i$, $c_j$ that of $j$, the sum goes over all $i$ and $j$ pairs of vertices, and $\delta(x,y)$ is 1 if $x=y$ and 0 otherwise.
If edge weights are given, then these are considered as the element of the $A$ adjacency matrix, and $k_i$ is the sum of weights of adjacent edges for vertex $i$.
modularity_matrix calculates the modularity matrix. This is a dense matrix,
and it is defined as the difference of the adjacency matrix and the
configuration model null model matrix. In other words element
$M_{ij}$ is given as $A_{ij}-d_i
d_j/(2m)$, where $A_{ij}$ is the (possibly
weighted) adjacency matrix, $d_i$ is the degree of vertex $i$,
and $m$ is the number of edges (or the total weights in the graph, if it
is weighed).
cluster_walktrap,
cluster_edge_betweenness,
cluster_fast_greedy, cluster_spinglass for
various community detection methods.g <- make_full_graph(5) %du% make_full_graph(5) %du% make_full_graph(5)
g <- add_edges(g, c(1,6, 1,11, 6, 11))
wtc <- cluster_walktrap(g)
modularity(wtc)
modularity(g, membership(wtc))Run the code above in your browser using DataCamp Workspace