face2face.statistics.network_quantities.variance_std_network

face2face.statistics.network_quantities.variance_std_network(network)

Calculate variance and standard deviation

Calculating the variance and the standard deviation of the degrees of a given network

\[\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})\]

\[\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}\]

Parameters

network (networkx Graph) – A graph with a specified degree sequence. Nodes are labeled based on the imported data set.

Returns

• var (float) – Contains the variance of the network degree

• std (float) – Contains the standard deviation of the network degree

Examples

>>> attr_list = ["ID", "Age", "Sex"]
>>> test_df = Data(path_tij="face2face/data/Test/tij_test.dat", separator_tij="\t",
>>>                path_meta="face2face/data/Test/meta_test.dat", separator_meta="\t",
>>>                meta_attr_list=attr_list)
>>> test_network = create_network_from_data(test_df)
>>> variance, standard_deviation = variance_std_network(test_network)
>>> print(variance)
0.2
>>> print(standard_deviation)
0.4472135954999579