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diff --git a/users/aspen/xanthous/test/Xanthous/Util/GraphSpec.hs b/users/aspen/xanthous/test/Xanthous/Util/GraphSpec.hs
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+++ b/users/aspen/xanthous/test/Xanthous/Util/GraphSpec.hs
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+module Xanthous.Util.GraphSpec (main, test) where
+--------------------------------------------------------------------------------
+import Test.Prelude
+--------------------------------------------------------------------------------
+import Xanthous.Util.Graph
+import Data.Graph.Inductive.Basic
+import Data.Graph.Inductive.Graph (labNodes, size, order)
+import Data.Graph.Inductive.PatriciaTree
+import Data.Graph.Inductive.Arbitrary
+--------------------------------------------------------------------------------
+
+main :: IO ()
+main = defaultMain test
+
+test :: TestTree
+test = testGroup "Xanthous.Util.Graph"
+  [ testGroup "mstSubGraph"
+    [ testProperty "always produces a subgraph"
+        $ \(CG _ (graph :: Gr Int Int)) ->
+          let msg = mstSubGraph $ undir graph
+          in counterexample (show msg)
+            $ msg `isSubGraphOf` undir graph
+    , testProperty "returns a graph with the same nodes"
+        $ \(CG _ (graph :: Gr Int Int)) ->
+          let msg = mstSubGraph graph
+          in counterexample (show msg)
+            $ labNodes msg === labNodes graph
+    , testProperty "has nodes - 1 edges"
+        $ \(CG _ (graph :: Gr Int Int)) ->
+          order graph > 1 ==>
+          let msg = mstSubGraph graph
+          in counterexample (show msg)
+            $ size msg === order graph - 1
+    , testProperty "always produces a simple graph"
+        $ \(CG _ (graph :: Gr Int Int)) ->
+          let msg = mstSubGraph graph
+          in counterexample (show msg) $ isSimple msg
+    ]
+  ]