diff --git a/pytato/analysis/__init__.py b/pytato/analysis/__init__.py
index fadf1c92d..cc367222d 100644
--- a/pytato/analysis/__init__.py
+++ b/pytato/analysis/__init__.py
@@ -33,7 +33,10 @@
 
 from pytato.array import (
     Array,
+    AxisPermutation,
+    BasicIndex,
     Concatenate,
+    DataWrapper as DataWrapper,
     DictOfNamedArrays,
     Einsum,
     IndexBase,
@@ -41,12 +44,18 @@
     IndexRemappingBase,
     InputArgumentBase,
     NamedArray,
+    Reshape,
     ShapeType,
     Stack,
 )
 from pytato.function import Call, FunctionDefinition, NamedCallResult
 from pytato.loopy import LoopyCall
-from pytato.transform import ArrayOrNames, CachedWalkMapper, Mapper
+from pytato.transform import (
+    ArrayOrNames,
+    CachedWalkMapper,
+    DependencyMapper as DependencyMapper,
+    Mapper,
+)
 
 
 if TYPE_CHECKING:
@@ -515,6 +524,118 @@ def get_node_multiplicities(
 # }}}
 
 
+# {{{ EdgeCountMapper
+
+@optimize_mapper(drop_args=True, drop_kwargs=True, inline_get_cache_key=True)
+class EdgeCountMapper(CachedWalkMapper):
+    """
+    Counts the number of edges in a DAG.
+
+    .. autoattribute:: edge_count
+    """
+
+    def __init__(self, count_duplicates: bool = False) -> None:
+        super().__init__()
+        self.edge_count: int = 0
+        self.count_duplicates = count_duplicates
+
+    def get_cache_key(self, expr: ArrayOrNames) -> int | ArrayOrNames:
+        # Each node is uniquely identified by its id
+        return id(expr) if self.count_duplicates else expr
+
+    def post_visit(self, expr: Any) -> None:
+        # Each dependency is connected by an edge
+        self.edge_count += len(self.get_dependencies(expr))
+
+    def get_dependencies(self, expr: Any) -> frozenset[Any]:
+        # Retrieve dependencies based on the type of the expression
+        if hasattr(expr, "bindings") or isinstance(expr, IndexLambda):
+            return frozenset(expr.bindings.values())
+        elif isinstance(expr, (BasicIndex, Reshape, AxisPermutation)):
+            return frozenset([expr.array])
+        elif isinstance(expr, Einsum):
+            return frozenset(expr.args)
+        return frozenset()
+
+
+def get_num_edges(outputs: Array | DictOfNamedArrays,
+                   count_duplicates: bool | None = None) -> int:
+    """
+    Returns the number of edges in DAG *outputs*.
+
+    Instances of `DictOfNamedArrays` are excluded from counting.
+    """
+    if count_duplicates is None:
+        from warnings import warn
+        warn(
+            "The default value of 'count_duplicates' will change "
+            "from True to False in 2025. "
+            "For now, pass the desired value explicitly.",
+            DeprecationWarning, stacklevel=2)
+        count_duplicates = True
+    from pytato.codegen import normalize_outputs
+    outputs = normalize_outputs(outputs)
+
+    ecm = EdgeCountMapper(count_duplicates)
+    ecm(outputs)
+
+    return ecm.edge_count
+
+# }}}
+
+
+# {{{ EdgeMultiplicityMapper
+
+
+class EdgeMultiplicityMapper(CachedWalkMapper):
+    """
+    Computes the multiplicity of each unique edge in a DAG.
+
+    The multiplicity of an edge is the number of times it appears in the DAG.
+
+    .. autoattribute:: edge_multiplicity_counts
+    """
+    def __init__(self) -> None:
+        from collections import defaultdict
+        super().__init__()
+        self.edge_multiplicity_counts: dict[tuple[Any, Any], int] = defaultdict(int)
+
+    def get_cache_key(self, expr: ArrayOrNames) -> int:
+        # Each node is uniquely identified by its id
+        return id(expr)
+
+    def post_visit(self, expr: Any) -> None:
+        dependencies = self.get_dependencies(expr)
+        for dep in dependencies:
+            self.edge_multiplicity_counts[dep, expr] += 1
+
+    def get_dependencies(self, expr: Any) -> frozenset[Any]:
+        # Retrieve dependencies based on the type of the expression
+        if hasattr(expr, "bindings") or isinstance(expr, IndexLambda):
+            return frozenset(expr.bindings.values())
+        elif isinstance(expr, (BasicIndex, Reshape, AxisPermutation)):
+            return frozenset([expr.array])
+        elif isinstance(expr, Einsum):
+            return frozenset(expr.args)
+        return frozenset()
+
+
+def get_edge_multiplicities(
+        outputs: Array | DictOfNamedArrays) -> dict[tuple[Any, Any], int]:
+    """
+    Returns the multiplicity per edge.
+    """
+    from pytato.codegen import normalize_outputs
+    outputs = normalize_outputs(outputs)
+
+    emm = EdgeMultiplicityMapper()
+    emm(outputs)
+
+    return emm.edge_multiplicity_counts
+
+# }}}
+
+
 # {{{ CallSiteCountMapper
 
 @optimize_mapper(drop_args=True, drop_kwargs=True, inline_get_cache_key=True)
diff --git a/test/test_pytato.py b/test/test_pytato.py
index f67e7e5f1..bcd875812 100644
--- a/test/test_pytato.py
+++ b/test/test_pytato.py
@@ -765,6 +765,126 @@ def test_large_dag_with_duplicates_count():
         dag, count_duplicates=False)
 
 
+def test_empty_dag_edge_count():
+    from pytato.analysis import get_edge_multiplicities, get_num_edges
+
+    empty_dag = pt.make_dict_of_named_arrays({})
+
+    # Verify that get_num_edges returns 0 for an empty DAG
+    assert get_num_edges(empty_dag, count_duplicates=False) == 0
+
+    counts = get_edge_multiplicities(empty_dag)
+    assert len(counts) == 0
+
+
+def test_single_node_dag_edge_count():
+    from pytato.analysis import get_edge_multiplicities, get_num_edges
+
+    data = np.random.rand(4, 4)
+    single_node_dag = pt.make_dict_of_named_arrays(
+        {"result": pt.make_data_wrapper(data)})
+
+    edge_counts = get_edge_multiplicities(single_node_dag)
+
+    # Assert that there are no edges in a single-node DAG
+    assert len(edge_counts) == 0
+
+    # Get total number of edges
+    total_edges = get_num_edges(single_node_dag, count_duplicates=False)
+
+    assert total_edges == 0
+
+
+def test_small_dag_edge_count():
+    from pytato.analysis import get_edge_multiplicities, get_num_edges
+
+    # Make a DAG using two nodes and one operation
+    a = pt.make_placeholder(name="a", shape=(2, 2), dtype=np.float64)
+    b = a + 1
+    dag = pt.make_dict_of_named_arrays({"result": b})   # b = a + 1
+
+    # Verify that get_num_edges returns 1 for a DAG with one edge
+    assert get_num_edges(dag, count_duplicates=False) == 1
+
+    counts = get_edge_multiplicities(dag)
+    assert len(counts) == 1
+    assert counts[a, b] == 1  # One edge between a and b
+
+
+def test_large_dag_edge_count():
+    from testlib import make_large_dag
+
+    from pytato.analysis import get_edge_multiplicities, get_num_edges
+
+    iterations = 100
+    dag = make_large_dag(iterations, seed=42)
+
+    # Verify that the number of edges is equal to the number of iterations
+    assert get_num_edges(dag, count_duplicates=False) == iterations
+
+    counts = get_edge_multiplicities(dag)
+    assert len(counts) == iterations
+
+
+def test_random_dag_edge_count():
+    from testlib import count_edges_using_dependency_mapper, get_random_pt_dag
+
+    from pytato.analysis import get_num_edges
+
+    for i in range(100):
+        dag = get_random_pt_dag(seed=i, axis_len=5)
+
+        edge_count = get_num_edges(dag, count_duplicates=False)
+
+        sum_edges = count_edges_using_dependency_mapper(dag)
+
+        assert edge_count == sum_edges
+
+
+def test_small_dag_with_duplicates_edge_count():
+    from testlib import make_small_dag_with_duplicates
+
+    from pytato.analysis import (
+        get_num_edges,
+    )
+
+    dag = make_small_dag_with_duplicates()
+
+    # Get the number of edges, including duplicates
+    edge_count = get_num_edges(dag, count_duplicates=True)
+    expected_edge_count = 3
+    assert edge_count == expected_edge_count
+
+
+def test_large_dag_with_duplicates_edge_count():
+    from testlib import make_large_dag_with_duplicates
+
+    from pytato.analysis import (
+        get_edge_multiplicities,
+        get_num_edges,
+    )
+
+    iterations = 100
+    dag = make_large_dag_with_duplicates(iterations, seed=42)
+
+    # Get the number of edges, including duplicates
+    edge_count = get_num_edges(dag, count_duplicates=True)
+
+    # Get the number of occurrences of each unique edge
+    edge_multiplicity = get_edge_multiplicities(dag)
+    assert any(count > 1 for count in edge_multiplicity.values())
+
+    expected_edge_count = sum(edge_multiplicity.values())
+    assert edge_count == expected_edge_count
+
+    # Check that duplicates are correctly calculated
+    num_duplicates = sum(count - 1 for count in edge_multiplicity.values())
+
+    # Ensure edge count is accurate
+    assert edge_count - num_duplicates == get_num_edges(
+        dag, count_duplicates=False)
+
+
 def test_rec_get_user_nodes():
     x1 = pt.make_placeholder("x1", shape=(10, 4))
     x2 = pt.make_placeholder("x2", shape=(10, 4))
diff --git a/test/testlib.py b/test/testlib.py
index 53bf79436..f3ee86ed8 100644
--- a/test/testlib.py
+++ b/test/testlib.py
@@ -16,12 +16,13 @@
     AxisPermutation,
     Concatenate,
     DataWrapper,
+    DictOfNamedArrays,
     Placeholder,
     Reshape,
     Roll,
     Stack,
 )
-from pytato.transform import Mapper
+from pytato.transform import ArrayOrNames, Mapper
 
 
 # {{{ tools for comparison to numpy
@@ -367,7 +368,6 @@ def make_small_dag_with_duplicates() -> pt.DictOfNamedArrays:
 def make_large_dag_with_duplicates(iterations: int,
                                    seed: int = 0) -> pt.DictOfNamedArrays:
 
-    random.seed(seed)
     rng = np.random.default_rng(seed)
     a = pt.make_placeholder(name="a", shape=(2, 2), dtype=np.float64)
     current = a
@@ -395,7 +395,22 @@ def make_large_dag_with_duplicates(iterations: int,
     result = pt.sum(combined_expr, axis=0)
     return pt.make_dict_of_named_arrays({"result": result})
 
-# }}}
+
+def count_edges_using_dependency_mapper(dag: ArrayOrNames | DictOfNamedArrays) -> int:
+    # Use DependencyMapper to find all nodes in the graph
+    dep_mapper = pt.transform.DependencyMapper()
+    all_nodes = dep_mapper(dag)
+
+    # Initialize edge count
+    edge_count = 0
+
+    # For each node, find its direct predecessors and count them as edges
+    pred_getter = pt.analysis.DirectPredecessorsGetter()
+    for node in all_nodes:
+        direct_predecessors = pred_getter(node)
+        edge_count += len(direct_predecessors)
+
+    return edge_count
 
 
 # {{{ tags used only by the regression tests