easygraph.functions.basic package

Submodules

easygraph.functions.basic.avg_degree module

easygraph.functions.basic.avg_degree.average_degree(G) → float

Returns the average degree of the graph.

Parameters:

G (graph) – A EasyGraph graph

Returns:

average degree – The average degree of the graph.

Return type:

float

Notes

Self loops are counted twice in the total degree of a node.

Examples

>>> G = eg.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge(1, 2)
>>> G.add_edge(2, 3)
>>> eg.average_degree(G)
1.3333333333333333

easygraph.functions.basic.cluster module

easygraph.functions.basic.cluster.average_clustering(G, nodes=None, weight=None, count_zeros=True, n_workers=None)

Compute the average clustering coefficient for the graph G.

The clustering coefficient for the graph is the average,

\[C = \frac{1}{n}\sum_{v \in G} c_v,\]

where \(n\) is the number of nodes in G.

Parameters:

• G (graph) –

• nodes (container of nodes, optional (default=all nodes in G)) – Compute average clustering for nodes in this container.

• weight (string or None, optional (default=None)) – The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1.

• count_zeros (bool) – If False include only the nodes with nonzero clustering in the average.

Returns:

avg – Average clustering

Return type:

float

Examples

>>> G = eg.complete_graph(5)
>>> print(eg.average_clustering(G))
1.0

Notes

This is a space saving routine; it might be faster to use the clustering function to get a list and then take the average.

Self loops are ignored.

References

[1]

Generalizations of the clustering coefficient to weighted complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela, K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007). http://jponnela.com/web_documents/a9.pdf

[2]

Marcus Kaiser, Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. https://arxiv.org/abs/0802.2512

easygraph.functions.basic.cluster.clustering(*args, **kwargs)

easygraph.functions.basic.localassort module

easygraph.functions.basic.localassort.localAssort(edgelist, node_attr, pr=array([0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]), undir=True, missingValue=-1)

Calculate the multiscale assortativity. You must ensure that the node index and node attribute index start from 0 :param edgelist: the network represented as an edge list,

i.e., a E x 2 array of node pairs

Parameters:

• node_attr (array_like) – n length array of node attribute values

• pr (array, optional) – array of one minus restart probabilities for the random walk in calculating the personalised pagerank. The largest of these values determines the accuracy of the TotalRank vector max(pr) -> 1 is more accurate (default: [0, .1, .2, .3, .4, .5, .6, .7, .8, .9])

• undir (bool, optional) – indicate if network is undirected (default: True)

• missingValue (int, optional) – token to indicate missing attribute values (default: -1)

Returns:

• assortM (array_like) – n x len(pr) array of local assortativities, each column corresponds to a value of the input restart probabilities, pr. Note if only number of restart probabilties is greater than one (i.e., len(pr) > 1).

• assortT (array_like) – n length array of multiscale assortativities

• Z (array_like) – N length array of per-node confidence scores

References

For full details see [1] .. [1] Peel, L., Delvenne, J. C., & Lambiotte, R. (2018). “Multiscale

mixing patterns in networks.’ PNAS, 115(16), 4057-4062.

easygraph.functions.basic.predecessor_path_based module

Module contents