Using Gephi Toolkit to compute the average degree of the given graph in the GraphML format.

avgdegree.groovy

#!/usr/bin/env groovy

import org.gephi.data.attributes.api.AttributeController
import org.gephi.graph.api.GraphController
import org.gephi.io.importer.api.EdgeDefault
import org.gephi.io.importer.api.ImportController
import org.gephi.io.processor.plugin.DefaultProcessor
import org.gephi.project.api.ProjectController
import org.gephi.statistics.plugin.Degree
import org.openide.util.Lookup

pc = Lookup.getDefault().lookup(ProjectController.class)
pc.newProject()
workspace = pc.getCurrentWorkspace()

importController = Lookup.getDefault().lookup(ImportController.class)
graphModel = Lookup.getDefault().lookup(GraphController.class).getModel()
attributeModel = Lookup.getDefault().lookup(AttributeController.class).getModel()

container = importController.importFile(new File(args[0]))
container.getLoader().setEdgeDefault(EdgeDefault.UNDIRECTED)
importController.process(container, new DefaultProcessor(), workspace)
graph = graphModel.getUndirectedGraph()

degree = new Degree()
degree.execute(graph.getGraphModel(), attributeModel)
println(degree.getAverageDegree())

Don't forget to place the gephi-toolkit.jar into the Groovy's lib/ folder.

$ ./avgdegree.groovy graph.graphml
# Nodes loaded: 65
# Edges loaded: 15
0.46153846153846156

Nice! A slightly more idiomatic Groovy version:

#!/usr/bin/env groovy

import org.gephi.data.attributes.api.AttributeController
import org.gephi.graph.api.GraphController
import org.gephi.io.importer.api.EdgeDefault
import org.gephi.io.importer.api.ImportController
import org.gephi.io.processor.plugin.DefaultProcessor
import org.gephi.project.api.ProjectController
import org.gephi.statistics.plugin.Degree
import org.openide.util.Lookup

pc = Lookup.default.lookup(ProjectController)
pc.newProject()
workspace = pc.currentWorkspace

importController = Lookup.default.lookup(ImportController)
graphModel = Lookup.default.lookup(GraphController).model
attributeModel = Lookup.default.lookup(AttributeController).model

container = importController.importFile(args[0] as File)
container.loader.edgeDefault = EdgeDefault.UNDIRECTED
importController.process(container, new DefaultProcessor(), workspace)
graph = graphModel.undirectedGraph

degree = new Degree()
degree.execute(graph.graphModel, attributeModel)
println(degree.averageDegree)

@melix, thank you!