analysis-languages.texw

<<echo = False>>=
import igraph
import numpy as np
import collections
from matrix2latex import matrix2latex

g = igraph.read('repositories.gml').components().giant()
@

We group repositories by language and first calculate the resulting modularity
using both the weighted and unweighted algorithms implemented in igraph; the
results are presented in table~\ref{tab:languageclustering}.

<<>>=
by_language = igraph.VertexClustering.FromAttribute(g, 'language')
mod_u = g.modularity(by_language)
mod_w = g.modularity(by_language, 'weight')
@

\begin{table}[h]
\centering
\caption{Properties of clustering by language.}
\begin{tabular}{l r}
\toprule
Unweighted modularity & <%= "%0.3f" % mod_u %> \\
Weighted modularity   & <%= "%0.3f" % mod_w %> \\
\bottomrule
\end{tabular}
\label{tab:languageclustering}
\end{table}

We then examine the language-based clusters as independent subgraphs, presented
in descending order of number of repositories. Measures of community
strength are calculated below and presented in
table~\ref{tab:clusteringcoefficient}: the density (fraction of possible edges
that exist) and forms of the clustering coefficient (probability that any two
neighbors of a node are themselves connected) for the entire subgraph, the
average for each node, and a variant of the latter that accounts for edge
weights.

<<>>=
langs = sorted(by_language.subgraphs(),
    key=lambda x: len(x.vs), reverse=True)
names = [s.vs[0]['language'].replace('#', '\#') for s in langs]
langs.append(g) # Include statistics on entire graph
names.append('OVERALL')

count_n = [len(s.vs)                   for s in langs]
count_e = [len(s.es)                   for s in langs]
density = [s.density()                 for s in langs]
tr      = [s.transitivity_undirected() for s in langs]
tr_avg  = [s.transitivity_avglocal_undirected(mode='zero')
    for s in langs]
tr_avgw = [s.transitivity_avglocal_undirected(mode='zero',
    weights='weight') for s in langs]
@

<%= matrix2latex([count_n, count_e, density, tr, tr_avg, tr_avgw],
    transpose=True,
    alignment="r",
    formatColumn=["$%d$", "$%d$", "$%.3f$", "$%.3f$", "$%.3f$", "$%.3f$"],
    headerColumn=names,
    headerRow=["Language", "Nodes", "Edges", "Density",
        "Global", "Local", "Weighted"],
    label="clusteringcoefficient", 
    caption="""Languages in the dataset, subgraph density and clustering
    coefficients (in averages, nodes with degree\\textless 2 treated as having
    clustering coefficient 0).""")%>