CODEWITHSUNDEEP
pythonnetworkx
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0x90

Reputation: 40982

Understanding average_degree_connectivity in networkx?

I have some hard time to understand this graph quantity: networkx.algorithms.assortativity.average_degree_connectivity

enter image description here

average_neighbor_degree returns a node id and its average_neighbor_degree:

d – A dictionary keyed by node with average neighbors degree value.

However, I can't understand what average_degree_connectivity is? It returns:

d – A dictionary keyed by degree k with the value of average connectivity.

For example, for three graphs the average_degree_connectivity vs. average neighbors degree value. look as follows. What does average neighbors degree value. mean? enter image description here

  1. What does average_degree_connectivity represent?
  2. How is average_neighbor_degree related to average_degree_connectivity?

Upvotes: 1

Views: 2753

Answers (1)

fynnlyte
fynnlyte

Reputation: 1029

It makes sense to answer your questions the other way round:

  • Let v be a vertex with m neighbors. The average_neighbor_degree of v is simply the sum of its neighbors' degrees divided by m.

  • For the average_degree_connectivity, this is the important part of the definition:

    ... is the average nearest neighbor degree of nodes with degree k

    So for all the different degrees that occur in the graph, it gives the average of the average_neighbor_degree of all nodes with the same degree. It is a measure of how connected nodes with certain degrees are.

That are many averages, I hope this snippet clarifies question 2:

import networkx as nx
from collections import defaultdict

G = nx.karate_club_graph()
avg_neigh_degrees = nx.algorithms.assortativity.average_neighbor_degree(G)
deg_to_avg_neighbor_degrees = defaultdict(list)
for node, degree in nx.degree(G):
    deg_to_avg_neighbor_degrees[degree].append(avg_neigh_degrees[node])

# this is the same as nx.algorithms.assortativity.average_degree_connectivity(G)
avg_degree_connectivity = {degree: sum(vals)/len(vals) for degree, vals in
                           deg_to_avg_neighbor_degrees.items()}

Upvotes: 3

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