--- a
+++ b/tests/graphs/test_object_api.py
@@ -0,0 +1,124 @@
+from pathaia.graphs import Graph, UGraph, Tree
+from pathaia.graphs.errors import InvalidTree
+from scipy.sparse import csr_matrix
+from pytest import raises, warns
+import itertools
+from ordered_set import OrderedSet
+
+
+def test_graph_init():
+    nodes_init = (None, (1, 2, 3), "123")
+    edges_init = (None, ((1, 3), (1, 2), (2, 1)))
+    A_init = (None, csr_matrix(((1, 1), ((0, 1), (1, 2))), shape=(3, 3), dtype=bool))
+
+    expected = (
+        (OrderedSet(), set(), csr_matrix((0, 0), dtype=bool)),
+        (
+            OrderedSet((0, 1, 2)),
+            {(0, 1), (1, 2)},
+            csr_matrix(((1, 1), ((0, 1), (1, 2))), shape=(3, 3), dtype=bool),
+        ),
+        (
+            OrderedSet((1, 3, 2)),
+            {(1, 3), (1, 2), (2, 1)},
+            csr_matrix(((1, 1, 1), ((0, 0, 2), (1, 2, 0))), shape=(3, 3), dtype=bool),
+        ),
+        (
+            OrderedSet((1, 3, 2)),
+            {(1, 3), (1, 2), (2, 1)},
+            csr_matrix(((1, 1, 1), ((0, 0, 2), (1, 2, 0))), shape=(3, 3), dtype=bool),
+        ),
+        (OrderedSet((1, 2, 3)), set(), csr_matrix((3, 3), dtype=bool)),
+        (
+            OrderedSet((1, 2, 3)),
+            {(1, 2), (2, 3)},
+            csr_matrix(((1, 1), ((0, 1), (1, 2))), shape=(3, 3), dtype=bool),
+        ),
+        (
+            OrderedSet((1, 2, 3)),
+            {(1, 3), (1, 2), (2, 1)},
+            csr_matrix(((1, 1, 1), ((0, 0, 1), (2, 1, 0))), shape=(3, 3), dtype=bool),
+        ),
+        (
+            OrderedSet((1, 2, 3)),
+            {(1, 3), (1, 2), (2, 1)},
+            csr_matrix(((1, 1, 1), ((0, 0, 1), (2, 1, 0))), shape=(3, 3), dtype=bool),
+        ),
+        (OrderedSet(("1", "2", "3")), set(), csr_matrix((3, 3), dtype=bool)),
+        (
+            OrderedSet(("1", "2", "3")),
+            {("1", "2"), ("2", "3")},
+            csr_matrix(((1, 1), ((0, 1), (1, 2))), shape=(3, 3), dtype=bool),
+        ),
+        KeyError,
+        KeyError,
+    )
+
+    for exp, (nodes, edges, A) in zip(
+        expected, itertools.product(nodes_init, edges_init, A_init)
+    ):
+        if isinstance(exp, tuple):
+            exp_nodes, exp_edges, exp_A = exp
+            G = Graph(nodes, edges, A)
+            assert G.nodes == exp_nodes
+            assert G.edges == exp_edges
+            assert (G.A[G.A > 0].A == exp_A[exp_A > 0].A).all()
+        else:
+            assert raises(exp, Graph, nodes, edges, A)
+
+
+def test_ugraph_init():
+    nodes = (1, 2, 3)
+    edges = ((1, 3), (1, 2), (2, 1))
+    A = None
+
+    exp_nodes, exp_edges, exp_A = (
+        OrderedSet((1, 2, 3)),
+        {(1, 2), (1, 3)},
+        csr_matrix(
+            ((1, 1, 1, 1), ((0, 1, 0, 2), (1, 0, 2, 0))), shape=(3, 3), dtype=bool
+        ),
+    )
+
+    G = UGraph(nodes, edges, A)
+    assert G.nodes == exp_nodes
+    assert G.edges == exp_edges
+    assert (G.A[G.A > 0].A == exp_A[exp_A > 0].A).all()
+
+
+def test_tree_init():
+    parents_init = (None, {2: 1, 3: 2, 4: 2})
+    children_init = (None, {1: [2], 2: [3, 4]}, {1: [3]})
+    edges_init = (None, ((1, 4), (2, 1)))
+
+    expected = (
+        (dict(), dict(), set()),
+        ({4: 1, 1: 2}, {1: {4}, 2: {1}}, {(1, 4), (2, 1)}),
+        ({2: 1, 3: 2, 4: 2}, {1: {2}, 2: {3, 4}}, {(1, 2), (2, 3), (2, 4)}),
+        ({4: 1, 1: 2}, {1: {4}, 2: {1}}, {(1, 4), (2, 1)}, UserWarning),
+        ({3: 1}, {1: {3}}, {(1, 3)}),
+        ({4: 1, 1: 2}, {1: {4}, 2: {1}}, {(1, 4), (2, 1)}, UserWarning),
+        ({2: 1, 3: 2, 4: 2}, {1: {2}, 2: {3, 4}}, {(1, 2), (2, 3), (2, 4)}),
+        ({4: 1, 1: 2}, {1: {4}, 2: {1}}, {(1, 4), (2, 1)}, UserWarning),
+        ({2: 1, 3: 2, 4: 2}, {1: {2}, 2: {3, 4}}, {(1, 2), (2, 3), (2, 4)}),
+        ({4: 1, 1: 2}, {1: {4}, 2: {1}}, {(1, 4), (2, 1)}, UserWarning),
+        InvalidTree,
+        ({4: 1, 1: 2}, {1: {4}, 2: {1}}, {(1, 4), (2, 1)}, UserWarning),
+    )
+
+    for exp, (parents, children, edges) in zip(
+        expected, itertools.product(parents_init, children_init, edges_init)
+    ):
+        if isinstance(exp, tuple):
+            if len(exp) == 3:
+                exp_parents, exp_children, exp_edges = exp
+                T = Tree(parents=parents, children=children, edges=edges)
+            else:
+                exp_parents, exp_children, exp_edges, warning = exp
+                with warns(warning):
+                    T = Tree(parents=parents, children=children, edges=edges)
+            assert T.parents == exp_parents
+            assert T.children == exp_children
+            assert T.edges == exp_edges
+        else:
+            assert raises(exp, Tree, parents=parents, children=children, edges=edges)