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I have some doubts with this measure.
In my directed graph the results of in degree and out degree are the same. It should not be the same.
Does anybody know how the calculation of this measure is made?

If you are talking about the Average In Degree and Average Out Degree calculated with the In/Out Degree statistic, it is normal to find identical values. They are calculated by summing the in degree (or out degree) value of each node that make the graph and dividing the final sum by the number of nodes.

With a directed graph: AvgInDegree = AvgOutDegree = NbEdges/NbNodes.

In a directed graph. The In Degree isnt the number of edges that arrives in one node? And the out degree isnt the number of edges that leaves a node?
If the calculation is the same why two different names to the same result? There is any case that the values are different?

You are correct about the definitions of In Degree and Out Degree. When running the In/Out Degree statistic, these two metrics are calculated for each node of the graph and displayed in the Data Laboratory and the Edit panel. The AvgInDegree and AvgOutDegree shown in the statisctic report are identical for a directed graph but the calculation done to obtain them is different. Therefore, I think that it is good to mention both. But I agree with you on the fact that it is a little misleading.

Quick additional question regarding the calculation of in and out degree...
I know that Gephi cannot show multiple connections between two nodes, and that it applies an algorithm to accommodate that fact by applying an edge weight value. However, does Gephi record the directionality of the edges that it is combining? i.e. when In Degree is calculated, is Gephi incorporating all of the data that was uploaded, or, a version based on the fewer edges that have been combined?

What does mean value and count in gephi statistics. I have 40 nodes and 42 edges. I cant read the meaning of value and count.I don't understand in what measures is that. Thank You