I have a simple directed network graph object G. It is created as follows:
import networkx as nx
G = nx.DiGraph()
nodes = ["A","B","C","D","E","F","G","H"]
G.add_nodes_from(nodes)
G.add_edges_from([("A","B"), ("A","C"),
("B","D"), ("B", "E"),
("C", "F"), ("C", "G"), ("C","H")])
pos = {"A":(10, 10),
"B":(7.5, 7.5), "C":(12.5, 7.5),
"D":(6, 6), "E":(9, 6),
"F":(11, 6), "G":(14, 6), "H":(17, 6)}
nx.draw_networkx(G, pos = pos, arrows = True,
node_shape = "s", node_color = "white")
It looks as shown below. A is the root node. B and C are intermediate nodes. And D, E, F, G, and H are leaves.
Closeness centrality is calculated as the average of the shortest path length from the node to every other node in the network according to this source page 27.
I can calculate the closeness centrality of this graph using nx.closeness_centrality(G). And I get the following results:
{'A': 0.0,
'B': 0.14285714285714285,
'C': 0.14285714285714285,
'D': 0.19047619047619047,
'E': 0.19047619047619047,
'F': 0.19047619047619047,
'G': 0.19047619047619047,
'H': 0.19047619047619047}
The closeness centrality of A is 0 because it is the root node. The closeness centrality of B and C are 1/7 because the distance from A is 1 and from all other nodes is 0. I think it is calculated as (1+0+0+0+0+0+0)/7. However, I cannot understand why the closeness centrality of other nodes is same. Their value is equivalent to 2/10.5. I am not sure how it is calculated.
Is it possible to show how the closeness centrality is calculated step by step rather than getting it directly from nx.closeness_centrality(G)?