I believe the results of closeness centrality produces incorrect results in the undirected, weighted, not fully connected graph case.

I can verify results from my algorithm with the networkX library used in python.

The graph and python code:

G = nx.Graph()

# add nodes
G.add_node(0, name="a")
G.add_node(1, name="b")
G.add_node(2, name="c")
G.add_node(3, name="d")
G.add_node(4, name="e")
G.add_node(5, name="f")
G.add_node(6, name="g")
G.add_node(7, name="h")
G.add_node(8, name="i")
G.add_node(9, name="j")
G.add_node(10, name="k")

# add edge from node 0 to node 1
G.add_edge(0, 1, weight=1)
G.add_edge(0, 2, weight=1)
G.add_edge(0, 4, weight=5)
G.add_edge(1, 2, weight=4)
G.add_edge(1, 4, weight=1)
G.add_edge(1, 6, weight=1)
G.add_edge(2, 4, weight=1)
G.add_edge(2, 3, weight=3)
G.add_edge(4, 3, weight=2)
G.add_edge(4, 6, weight=2)
G.add_edge(3, 6, weight=5)
G.add_edge(3, 5, weight=1)
G.add_edge(6, 5, weight=1)
G.add_edge(7, 8, weight=3)
G.add_edge(8, 9, weight=3)

print(nx.closeness_centrality(G, distance="weight", wf_improved=False))

Expected Behavior

Closeness Centrality produces these values:
{0: 0.46153846153846156, 1: 0.6, 2: 0.42857142857142855, 3: 0.4, 4: 0.5454545454545454, 5: 0.42857142857142855, 6: 0.5454545454545454, 7: 0.2222222222222222, 8: 0.3333333333333333, 9: 0.2222222222222222, 10: 0.0}

Current Behavior

Gephi produces these values: {0: 0.6, 1: 0.75, 2: 0.75, 3: 0.75, 4: 0.857143, 5: 0.545455, 6: 0.75, 7: 0.6667, 8: 1.0, 9: 0.6667, 10: 0.0}

Possible Solution

Revisit the algorithm and examine what it is doing in the case where the graph is undirected, weighted, and not fully connected.

Steps to Reproduce

Attached is the file of the graph thats producing perceived incorrect results.ClosenessGraph.csv

1. Create the above graph in the Gephi application
2. Run Network Diameter with: Directed selected and Normalize Centralities in [0,1] set to true
3. Use Data Laboratory to inspect closeness column

Context

Trying to verify results for the algorithms that I am building for a client project. This feature works in the other case combinations of: directed, undirected, weighted, unweighted, fully connected, not fully connected but fails in the above scenario.

Your Environment

I am using Gephi application on Windows 11

• Version used: Gephi 0.10.1
• Operating System: Windows 11.0