diff --git a/pyomo/util/graph.py b/pyomo/util/graph.py
index 0f802accc96..80d3db0b909 100644
--- a/pyomo/util/graph.py
+++ b/pyomo/util/graph.py
@@ -49,9 +49,16 @@ def graph_from_pyomo(m: _BlockData,
 def plot_pyomo_model(m: _BlockData,
                      include_objective: bool = True,
                      active: bool = True,
-                     plot_title: Optional[str] = None):
+                     plot_title: Optional[str] = None,
+                     bipartite_plot: bool = False,
+                     show_plot: bool = True):
     graph = graph_from_pyomo(m, include_objective=include_objective, active=active)
-    pos_dict = nx.drawing.spring_layout(graph, seed=0)
+    if bipartite_plot:
+        left_nodes = [c for c in OrderedSet(m.component_data_objects(pe.Constraint, descend_into=True, active=active))]
+        left_nodes.extend(_CompNode(obj) for obj in ComponentSet(m.component_data_objects(pe.Objective, descend_into=True, active=active)))
+        pos_dict = nx.drawing.bipartite_layout(graph, nodes=left_nodes)
+    else:
+        pos_dict = nx.drawing.spring_layout(graph, seed=0)
 
     edge_x = list()
     edge_y = list()
@@ -99,4 +106,5 @@ def plot_pyomo_model(m: _BlockData,
     fig = go.Figure(data=[edge_trace, node_trace])
     if plot_title is not None:
         fig.update_layout(title=dict(text=plot_title))
-    fig.show()
+    if show_plot:  # this option is mostly for unit tests
+        fig.show()
diff --git a/pyomo/util/tests/test_graph.py b/pyomo/util/tests/test_graph.py
new file mode 100644
index 00000000000..c9bc7d306cf
--- /dev/null
+++ b/pyomo/util/tests/test_graph.py
@@ -0,0 +1,26 @@
+import pyomo.environ as pe
+from pyomo.common import unittest
+from pyomo.common.dependencies import attempt_import
+nx, nx_available = attempt_import('networkx')
+plotly, plotly_available = attempt_import('plotly')
+
+
+@unittest.skipUnless(nx_available, 'plot_pyomo_model requires networkx')
+@unittest.skipUnless(plotly_available, 'plot_pyomo_model requires plotly')
+class TestPlotPyomoModel(unittest.TestCase):
+    def test_plot_pyomo_model(self):
+        """
+        Unfortunately, this test only ensures the code runs without errors.
+        It does not test for correctness.
+        """
+        m = pe.ConcreteModel()
+        m.x = pe.Var(bounds=(-1, 1))
+        m.y = pe.Var()
+        m.z = pe.Var()
+        m.obj = pe.Objective(expr=m.y**2 + m.z**2)
+        m.c1 = pe.Constraint(expr=m.y == 2*m.x + 1)
+        m.c2 = pe.Constraint(expr=m.z >= m.x)
+        from pyomo.util.graph import plot_pyomo_model
+        plot_pyomo_model(m, plot_title='test plot', bipartite_plot=False, show_plot=False)
+        plot_pyomo_model(m, plot_title='test plot', bipartite_plot=True, show_plot=False)
+