diff --git a/pydatastructs/graphs/__init__.py b/pydatastructs/graphs/__init__.py
index bdfebdc72..ad6006342 100644
--- a/pydatastructs/graphs/__init__.py
+++ b/pydatastructs/graphs/__init__.py
@@ -17,7 +17,8 @@
     shortest_paths,
     all_pair_shortest_paths,
     topological_sort,
-    topological_sort_parallel
+    topological_sort_parallel,
+    max_flow
 )
 
 __all__.extend(algorithms.__all__)
diff --git a/pydatastructs/graphs/algorithms.py b/pydatastructs/graphs/algorithms.py
index 234255008..85a0c6ae7 100644
--- a/pydatastructs/graphs/algorithms.py
+++ b/pydatastructs/graphs/algorithms.py
@@ -22,7 +22,8 @@
     'shortest_paths',
     'all_pair_shortest_paths',
     'topological_sort',
-    'topological_sort_parallel'
+    'topological_sort_parallel',
+    'max_flow'
 ]
 
 Stack = Queue = deque
@@ -1064,3 +1065,56 @@ def _job(graph: Graph, u: str):
     if len(L) != num_vertices:
         raise ValueError("Graph is not acyclic.")
     return L
+
+
+def _breadth_first_search_max_flow(graph: Graph, source_node, sink_node, flow_passed):
+    bfs_queue = Queue()
+    parent, currentPathC = {}, {}
+    parent[source_node] = -2
+    currentPathC[source_node] = float('inf')
+    bfs_queue.append(source_node)
+    while len(bfs_queue) != 0:
+        curr_node = bfs_queue.popleft()
+        next_nodes = graph.neighbors(curr_node)
+        if len(next_nodes) != 0:
+            for next_node in next_nodes:
+                capacity = graph.get_edge(curr_node, next_node.name).value
+                fp = flow_passed.get((curr_node, next_node.name), 0)
+                if capacity and parent.get(next_node.name, False) is False and capacity - fp> 0:
+                    parent[next_node.name] = curr_node
+                    next_flow = min(currentPathC[curr_node], capacity - fp)
+                    currentPathC[next_node.name] = next_flow
+                    if next_node.name == sink_node:
+                        return (next_flow, parent)
+                    bfs_queue.append(next_node.name)
+    return (0, parent)
+
+
+def _max_flow_edmonds_karp_(graph: Graph, source, sink):
+    m_flow = 0
+    flow_passed = {}
+    new_flow, parent = _breadth_first_search_max_flow(graph, source, sink, flow_passed)
+    while new_flow != 0:
+        m_flow += new_flow
+        current = sink
+        while current != source:
+            prev = parent[current]
+            fp = flow_passed.get((prev, current), 0)
+            flow_passed[(prev, current)] = fp + new_flow
+            fp = flow_passed.get((current, prev), 0)
+            flow_passed[(current, prev)] = fp - new_flow
+            current = prev
+        new_flow, parent = _breadth_first_search_max_flow(graph, source, sink, flow_passed)
+    return m_flow
+
+def max_flow(graph, source, sink, algorithm='edmonds_karp', **kwargs):
+    raise_if_backend_is_not_python(
+        max_flow, kwargs.get('backend', Backend.PYTHON))
+
+    import pydatastructs.graphs.algorithms as algorithms
+    func = "_max_flow_" + algorithm + "_"
+    if not hasattr(algorithms, func):
+        raise NotImplementedError(
+        f"Currently {algorithm} algorithm isn't implemented for "
+        "performing max flow on graphs.")
+    return getattr(algorithms, func)(graph, source, sink)
diff --git a/pydatastructs/graphs/tests/test_algorithms.py b/pydatastructs/graphs/tests/test_algorithms.py
index ddf274d1d..af9d13036 100644
--- a/pydatastructs/graphs/tests/test_algorithms.py
+++ b/pydatastructs/graphs/tests/test_algorithms.py
@@ -2,7 +2,7 @@
 breadth_first_search_parallel, minimum_spanning_tree,
 minimum_spanning_tree_parallel, strongly_connected_components,
 depth_first_search, shortest_paths, topological_sort,
-topological_sort_parallel)
+topological_sort_parallel, max_flow)
 from pydatastructs.utils.raises_util import raises
 
 def test_breadth_first_search():
@@ -369,3 +369,70 @@ def _test_topological_sort(func, ds, algorithm, threads=None):
 
     _test_topological_sort(topological_sort, "List", "kahn")
     _test_topological_sort(topological_sort_parallel, "List", "kahn", 3)
+
+
+def test_max_flow():
+    def _test_max_flow(ds, algorithm):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+
+        a = GraphNode('a')
+        b = GraphNode('b')
+        c = GraphNode('c')
+        d = GraphNode('d')
+        e = GraphNode('e')
+
+        G = Graph(a, b, c, d, e)
+
+        G.add_edge('a', 'b', 3)
+        G.add_edge('a', 'c', 4)
+        G.add_edge('b', 'c', 2)
+        G.add_edge('b', 'd', 3)
+        G.add_edge('c', 'd', 1)
+        G.add_edge('d', 'e', 6)
+
+        assert max_flow(G, 'a', 'e', algorithm) == 4
+        assert max_flow(G, 'a', 'c', algorithm) == 6
+
+        a = GraphNode('a')
+        b = GraphNode('b')
+        c = GraphNode('c')
+        d = GraphNode('d')
+        e = GraphNode('e')
+        f = GraphNode('f')
+
+        G2 = Graph(a, b, c, d, e, f)
+
+        G2.add_edge('a', 'b', 16)
+        G2.add_edge('a', 'c', 13)
+        G2.add_edge('b', 'c', 10)
+        G2.add_edge('b', 'd', 12)
+        G2.add_edge('c', 'b', 4)
+        G2.add_edge('c', 'e', 14)
+        G2.add_edge('d', 'c', 9)
+        G2.add_edge('d', 'f', 20)
+        G2.add_edge('e', 'd', 7)
+        G2.add_edge('e', 'f', 4)
+
+        assert max_flow(G2, 'a', 'f', algorithm) == 23
+        assert max_flow(G2, 'a', 'd', algorithm) == 19
+
+        a = GraphNode('a')
+        b = GraphNode('b')
+        c = GraphNode('c')
+        d = GraphNode('d')
+
+        G3 = Graph(a, b, c, d)
+
+        G3.add_edge('a', 'b', 3)
+        G3.add_edge('a', 'c', 2)
+        G3.add_edge('b', 'c', 2)
+        G3.add_edge('b', 'd', 3)
+        G3.add_edge('c', 'd', 2)
+
+        assert max_flow(G3, 'a', 'd', algorithm) == 5
+        assert max_flow(G3, 'a', 'b', algorithm) == 3
+
+
+    _test_max_flow("List", "edmonds_karp")
+    _test_max_flow("Matrix", "edmonds_karp")