Create a complete graph of lines between a set of points in QGIS

complete_graph.py

from itertools import combinations

# get the active layer
inlayer = iface.activeLayer()

# Get the index of the NAME field, then rewind the list
infeatures = inlayer.getFeatures()
eg = infeatures.next()
i = eg.fields().indexFromName('NAME')
infeatures.rewind()

# get the active layer's crs
crs = inlayer.crs().geographicCRSAuthId()

# create the new layer and start editing it
defstring = "LineString?crs=" + crs + "&field=id:integer&field=from:string(20)&field=to:string(20)&index=yes"
layer = QgsVectorLayer(defstring, "complete_graph", "memory")
layer.startEditing()

# Get every combination of points
pairs = combinations(infeatures, 2)
n = 0

for start, end in pairs:
    if start == end:  # don't create lines with length 0
        continue

    # hey, this API isn't super-simple
    startgeo, endgeo = start.geometry().asPoint(), end.geometry().asPoint()
    line = QgsGeometry.fromPolyline([QgsPoint(*startgeo), QgsPoint(*endgeo)])

    # Add feature to layer
    feature = QgsFeature()
    feature.setGeometry(line)

    feature.setAttributes([n, start.attributes()[i], end.attributes()[i]])

    layer.dataProvider().addFeatures([feature])

    # use this for testing
    #n = n + 1
    #if n > 10:
    #    break

layer.updateExtents()
layer.commitChanges()

QgsMapLayerRegistry.instance().addMapLayer(layer)

print 'layer is valid:', layer.isValid()

error = QgsVectorFileWriter.writeAsVectorFormat(
    layer,
    "/full/path/to/a/file/complete.shp",
    "CP1250",
    None,
    "ESRI Shapefile"
)

if error == QgsVectorFileWriter.NoError:
    print "success!"
else:
    print 'error'
    print error