upxo.netops.kchar module

Characterise NetworkX grain-neighbour graphs (degree distributions, etc.).

Companion to upxo.netops.kmake (graph build) and upxo.netops.kcmp (graph comparison) for KREPR / network representativeness studies.

upxo.netops.kchar.calculate_kdegrees(networks)

Get degree distribution of every network graph in networks.

Parameters:

networks (list) – List of networkx network graphs.

Returns:

• kd (list) – List of list of degree of every node in each network graph.

• Data structures

• —————

• networks = [k1, k2, …, kp, … kP] – Where, kp: pth network graph

• ks = [k1d, k2d, …, kid, …, knd] – Where, kid: degree distribution of ith network.

• kid = [dn1, dn2, …, dnj,… dnJ] – Where, dnj: degree of node j.

upxo.netops.kchar.calculate_kdegrees_equalbinning(networks)

Calculate the pairwise degree distributions, and equally bin them.

Parameters:

• tgt_graph (networkx graph) – Target graon structure O(n) neighbour network graph.

• smp_graph (networkx graph) – Sample graon structure O(n) neighbour network graph.

Returns:

• kd_tgt (List of degree of every node in target network.)

• kd_smp (List of degree of every node in sample network.)

• Data structures

• —————

• networks = [k1, k2, …, kp, … kP] – Where, kp: pth network graph

• ks = [k1d, k2d, …, kid, …, knd] – Where, kid: degree distribution of ith network.

• kid = [dn1, dn2, …, dnj,… dnJ] – Where, dnj: degree of node j.

• Explanations

• ————

• Some tests are sensitive to differences in the cumulative

• distribution functions (CDFs) of the data. Directly using the raw

• degree sequences can be misleading if the sample sizes

• (number of nodes) differ significantly between the two networks.

• Histograms normalize the data, providing a better representation of

• the underlying probability distributions.