graph_tool.correlations.avg_neighbor_corr

graph_tool.correlations.avg_neighbor_corr(g, deg_source, deg_target, bins=[0, 1], weight=None)

Obtain the average neighbor-neighbor correlation for the given graph.

Parameters:

gGraph

Graph to be used.

deg_sourcestring or VertexPropertyMap

degree type (“in”, “out” or “total”) or vertex property map for the source vertex.

deg_targetstring or VertexPropertyMap

degree type (“in”, “out” or “total”) or vertex property map for the target vertex.

binslist (optional, default: [0, 1])

Bins to be used for the source degrees. If the list has size 2, it is used as the constant width of an automatically generated bin range, starting from the first value.

weightedge property map (optional, default: None)

Weight (multiplicative factor) to be used on each edge.

Returns:

bin_avgnumpy.ndarray

Array with the deg_target average for the get_source bins.

bin_devnumpy.ndarray

Array with the standard deviation of the deg_target average for the get_source bins.

binsnumpy.ndarray

Source degree bins,

See also

assortativity

assortativity coefficient

scalar_assortativity

scalar assortativity coefficient

corr_hist

vertex-vertex correlation histogram

combined_corr_hist

combined single-vertex correlation histogram

avg_neighbor_corr

average nearest-neighbor correlation

avg_combined_corr

average combined single-vertex correlation

Notes

The average correlation is the average, for every vertex with degree (or scalar property) ‘source_deg’, the of the ‘target_deg’ degree (or scalar property) of its neighbors.

If enabled during compilation, this algorithm runs in parallel.

Examples

>>> def sample_k(max):
...     accept = False
...     while not accept:
...         k = np.random.randint(1,max+1)
...         accept = np.random.random() < 1.0 / k
...     return k
...
>>> g = gt.random_graph(10000, lambda: sample_k(40),
...                     model="probabilistic-configuration",
...                     edge_probs=lambda i, j: (sin(i / pi) * sin(j / pi) + 1) / 2,
...                     directed=False, n_iter=100)
>>> h = gt.avg_neighbor_corr(g, "out", "out")
>>> clf()
>>> xlabel("Source out-degree")
Text(...)
>>> ylabel("Target out-degree")
Text(...)
>>> errorbar(h[2][:-1], h[0], yerr=h[1], fmt="o")
<...>
>>> savefig("avg_corr.svg")

Average out/out degree correlation.