diff --git a/pydatastructs/graphs/__init__.py b/pydatastructs/graphs/__init__.py
new file mode 100644
index 000000000..a484339a9
--- /dev/null
+++ b/pydatastructs/graphs/__init__.py
@@ -0,0 +1,13 @@
+__all__ = []
+
+from . import graph
+from .graph import (
+    Graph
+)
+__all__.extend(graph.__all__)
+
+from . import adjacency_list
+from .adjacency_list import (
+    AdjacencyList
+)
+__all__.extend(adjacency_list.__all__)
diff --git a/pydatastructs/graphs/adjacency_list.py b/pydatastructs/graphs/adjacency_list.py
new file mode 100644
index 000000000..9adc6a383
--- /dev/null
+++ b/pydatastructs/graphs/adjacency_list.py
@@ -0,0 +1,55 @@
+from pydatastructs.graphs.graph import Graph
+from pydatastructs.linear_data_structures import DynamicOneDimensionalArray
+
+__all__ = [
+    'AdjacencyList'
+]
+
+class AdjacencyList(Graph):
+    """
+    Adjacency list implementation of graphs.
+
+    See also
+    ========
+
+    pydatastructs.graphs.graph.Graph
+    """
+    def __new__(cls, *vertices):
+        obj = object.__new__(cls)
+        for vertex in vertices:
+            obj.__setattr__(vertex.name, vertex)
+        obj.vertices = set([vertex.name for vertex in vertices])
+        return obj
+
+    def is_adjacent(self, node1, node2):
+        node1 = self.__getattribute__(node1)
+        return hasattr(node1, node2)
+
+    def neighbors(self, node):
+        node = self.__getattribute__(node)
+        return [self.__getattribute__(name) for name in node.adjacent]
+
+    def add_vertex(self, node):
+        self.vertices.add(node.name)
+        self.__setattr__(node.name, node)
+
+    def remove_vertex(self, name):
+        delattr(self, name)
+        self.vertices.remove(name)
+        for node in self.vertices:
+            node_obj = self.__getattribute__(node)
+            if hasattr(node_obj, name):
+                delattr(node_obj, name)
+                node_obj.adjacent.remove(name)
+
+    def add_edge(self, source, target):
+        source, target = self.__getattribute__(source), \
+                         self.__getattribute__(target)
+        source.__setattr__(target.name, target)
+        source.adjacent.add(target.name)
+
+    def remove_edge(self, source, target):
+        source, target = self.__getattribute__(source), \
+                         self.__getattribute__(target)
+        source.adjacent.remove(target.name)
+        delattr(source, target.name)
diff --git a/pydatastructs/graphs/graph.py b/pydatastructs/graphs/graph.py
new file mode 100644
index 000000000..188ec3929
--- /dev/null
+++ b/pydatastructs/graphs/graph.py
@@ -0,0 +1,103 @@
+
+__all__ = [
+    'Graph'
+]
+
+class Graph(object):
+    """
+    Represents generic concept of graphs.
+
+    Parameters
+    ==========
+
+    implementation: str
+        The implementation to be used for storing
+        graph in memory.
+        By default, 'adjacency_list'
+    vertices: AdjacencyListGraphNode(s)
+        For AdjacencyList implementation vertices
+        can be passed for initializing the graph.
+
+    Examples
+    ========
+
+    >>> from pydatastructs.graphs import Graph
+    >>> from pydatastructs.utils import AdjacencyListGraphNode
+    >>> v_1 = AdjacencyListGraphNode('v_1', 1)
+    >>> v_2 = AdjacencyListGraphNode('v_2', 2)
+    >>> g = Graph(v_1, v_2)
+    >>> g.add_edge('v_1', 'v_2')
+    >>> g.add_edge('v_2', 'v_1')
+    >>> g.is_adjacent('v_1', 'v_2')
+    True
+    >>> g.is_adjacent('v_2', 'v_1')
+    True
+    >>> g.remove_edge('v_1', 'v_2')
+    >>> g.is_adjacent('v_1', 'v_2')
+    False
+    >>> g.is_adjacent('v_2', 'v_1')
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Graph_(abstract_data_type)
+    """
+    def __new__(cls, *args, **kwargs):
+        implementation = kwargs.get('implementation', 'adjacency_list')
+        if implementation is 'adjacency_list':
+            from pydatastructs.graphs.adjacency_list import AdjacencyList
+            return AdjacencyList(*args)
+        else:
+            raise NotImplementedError("%s implementation is not a part "
+                                      "of the library currently."%(implementation))
+
+    def is_adjacent(self, node1, node2):
+        """
+        Checks if the nodes with the given
+        with the given names are adjacent
+        to each other.
+        """
+        raise NotImplementedError(
+            "This is an abstract method.")
+
+    def neighbors(self, node):
+        """
+        Lists the neighbors of the node
+        with given name.
+        """
+        raise NotImplementedError(
+            "This is an abstract method.")
+
+    def add_vertex(self, node):
+        """
+        Adds the input vertex to the node.
+        """
+        raise NotImplementedError(
+            "This is an abstract method.")
+
+    def remove_vertex(self, node):
+        """
+        Removes the input vertex along with all the edges
+        pointing towards to it.
+        """
+        raise NotImplementedError(
+            "This is an abstract method.")
+
+    def add_edge(self, source, target):
+        """
+        Adds the edge starting at first parameter
+        i.e., source and ending at the second
+        parameter i.e., target.
+        """
+        raise NotImplementedError(
+            "This is an abstract method.")
+
+    def remove_edge(self, source, target):
+        """
+        Removes the edge starting at first parameter
+        i.e., source and ending at the second
+        parameter i.e., target.
+        """
+        raise NotImplementedError(
+            "This is an abstract method.")
diff --git a/pydatastructs/graphs/tests/__init__.py b/pydatastructs/graphs/tests/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/pydatastructs/graphs/tests/test_adjacency_list.py b/pydatastructs/graphs/tests/test_adjacency_list.py
new file mode 100644
index 000000000..5581e1430
--- /dev/null
+++ b/pydatastructs/graphs/tests/test_adjacency_list.py
@@ -0,0 +1,34 @@
+from pydatastructs.graphs import Graph
+from pydatastructs.utils import AdjacencyListGraphNode
+
+def test_adjacency_list():
+    v_1 = AdjacencyListGraphNode('v_1', 1)
+    v_2 = AdjacencyListGraphNode('v_2', 2)
+    g = Graph(v_1, v_2, implementation='adjacency_list')
+    v_3 = AdjacencyListGraphNode('v_3', 3)
+    g.add_vertex(v_2)
+    g.add_vertex(v_3)
+    g.add_edge('v_1', 'v_2')
+    g.add_edge('v_2', 'v_3')
+    g.add_edge('v_3', 'v_1')
+    assert g.is_adjacent('v_1', 'v_2') is True
+    assert g.is_adjacent('v_2', 'v_3') is True
+    assert g.is_adjacent('v_3', 'v_1') is True
+    assert g.is_adjacent('v_2', 'v_1') is False
+    assert g.is_adjacent('v_3', 'v_2') is False
+    assert g.is_adjacent('v_1', 'v_3') is False
+    neighbors = g.neighbors('v_1')
+    assert neighbors == [v_2]
+    v = AdjacencyListGraphNode('v', 4)
+    g.add_vertex(v)
+    g.add_edge('v_1', 'v')
+    g.add_edge('v_2', 'v')
+    g.add_edge('v_3', 'v')
+    assert g.is_adjacent('v_1', 'v') is True
+    assert g.is_adjacent('v_2', 'v') is True
+    assert g.is_adjacent('v_3', 'v') is True
+    g.remove_edge('v_1', 'v')
+    assert g.is_adjacent('v_1', 'v') is False
+    g.remove_vertex('v')
+    assert g.is_adjacent('v_2', 'v') is False
+    assert g.is_adjacent('v_3', 'v') is False
diff --git a/pydatastructs/utils/__init__.py b/pydatastructs/utils/__init__.py
index 37e2067b9..bb63db83e 100644
--- a/pydatastructs/utils/__init__.py
+++ b/pydatastructs/utils/__init__.py
@@ -4,6 +4,9 @@
 from .misc_util import (
     TreeNode,
     LinkedListNode,
-    BinomialTreeNode
+    BinomialTreeNode,
+    AdjacencyListGraphNode,
+    AdjacencyMatrixGraphNode,
+    GraphEdge
 )
 __all__.extend(misc_util.__all__)
diff --git a/pydatastructs/utils/misc_util.py b/pydatastructs/utils/misc_util.py
index d13182f59..419d7d098 100644
--- a/pydatastructs/utils/misc_util.py
+++ b/pydatastructs/utils/misc_util.py
@@ -1,7 +1,10 @@
 __all__ = [
     'TreeNode',
     'LinkedListNode',
-    'BinomialTreeNode'
+    'BinomialTreeNode',
+    'AdjacencyListGraphNode',
+    'AdjacencyMatrixGraphNode',
+    'GraphEdge'
 ]
 
 _check_type = lambda a, t: isinstance(a, t)
@@ -34,7 +37,7 @@ class TreeNode(Node):
                  'height', 'parent', 'size']
 
     def __new__(cls, key, data):
-        obj = object.__new__(cls)
+        obj = Node.__new__(cls)
         obj.data, obj.key = data, key
         obj.left, obj.right, obj.parent, obj.height, obj.size = \
             None, None, None, 0, 1
@@ -78,7 +81,7 @@ class BinomialTreeNode(TreeNode):
 
     def __new__(cls, key, data):
         from pydatastructs.linear_data_structures.arrays import DynamicOneDimensionalArray
-        obj = object.__new__(cls)
+        obj = Node.__new__(cls)
         obj.data, obj.key = data, key
         obj.children, obj.parent, obj.is_root = (
         DynamicOneDimensionalArray(BinomialTreeNode, 0),
@@ -112,7 +115,7 @@ class LinkedListNode(Node):
         Any valid data to be stored in the node.
     """
     def __new__(cls, data=None, links=['next'], addrs=[None]):
-        obj = object.__new__(cls)
+        obj = Node.__new__(cls)
         obj.data = data
         for link, addr in zip(links, addrs):
             obj.__setattr__(link, addr)
@@ -121,3 +124,102 @@ def __new__(cls, data=None, links=['next'], addrs=[None]):
 
     def __str__(self):
         return str(self.data)
+
+class GraphNode(Node):
+    """
+    Abastract class for graph nodes/vertices.
+    """
+    def __str__(self):
+        return str((self.name, self.data))
+
+class AdjacencyListGraphNode(GraphNode):
+    """
+    Represents nodes for adjacency list implementation
+    of graphs.
+
+    Parameters
+    ==========
+
+    name: str
+        The name of the node by which it is identified
+        in the graph. Must be unique.
+    data
+        The data to be stored at each graph node.
+    adjacency_list: iterator
+        Any valid iterator to initialize the adjacent
+        nodes of the current node.
+        Optional, by default, None
+    """
+    def __new__(cls, name, data, adjacency_list=None):
+        obj = GraphNode.__new__(cls)
+        obj.name, obj.data = name, data
+        if adjacency_list is not None:
+            for node in adjacency_list:
+                obj.__setattr__(node.name, node)
+        obj.adjacent = set(adjacency_list) if adjacency_list is not None \
+                       else set()
+        return obj
+
+    def add_adjacent_node(self, name, data):
+        """
+        Adds adjacent node to the current node's
+        adjacency list with given name and data.
+        """
+        if hasattr(self, name):
+            getattr(self, name).data = data
+        else:
+            new_node = AdjacencyListGraphNode(name, data)
+            self.__setattr__(new_node.name, new_node)
+            self.adjacent.add(new_node.name)
+
+    def remove_adjacent_node(self, name):
+        """
+        Removes node with given name from
+        adjacency list.
+        """
+        if not hasattr(self, name):
+            raise ValueError("%s is not adjacent to %s"%(name, self.name))
+        self.adjacent.remove(name)
+        delattr(self, name)
+
+class AdjacencyMatrixGraphNode(GraphNode):
+    """
+    Represents nodes for adjacency matrix implementation
+    of graphs.
+
+    Parameters
+    ==========
+
+    name: str
+        The name of the node by which it is identified
+        in the graph. Must be unique.
+    data
+        The data to be stored at each graph node.
+    """
+    __slots__ = ['name', 'data']
+
+    def __new__(cls, name, data):
+        obj = GraphNode.__new__(cls)
+        obj.name, obj.data = name, data
+        return obj
+
+class GraphEdge(object):
+    """
+    Represents the concept of edges in graphs.
+
+    Parameters
+    ==========
+
+    node1: GraphNode or it's child classes
+        The source node of the edge.
+    node2: GraphNode or it's child classes
+        The target node of the edge.
+    """
+    def __new__(cls, node1, node2, value=None):
+        obj = object.__new__(cls)
+        obj.source, obj.target = node1, node2
+        obj.value = value
+        return obj
+
+    def __str__(self):
+        return str((self.source.name, self.target.name))
diff --git a/pydatastructs/utils/tests/test_misc_util.py b/pydatastructs/utils/tests/test_misc_util.py
new file mode 100644
index 000000000..f699ed748
--- /dev/null
+++ b/pydatastructs/utils/tests/test_misc_util.py
@@ -0,0 +1,27 @@
+from pydatastructs.utils import AdjacencyListGraphNode, AdjacencyMatrixGraphNode, GraphEdge
+from pydatastructs.utils.raises_util import raises
+
+def test_AdjacencyListGraphNode():
+    g_1 = AdjacencyListGraphNode('g_1', 1)
+    g_2 = AdjacencyListGraphNode('g_2', 2)
+    g = AdjacencyListGraphNode('g', 0, adjacency_list=[g_1, g_2])
+    g.add_adjacent_node('g_3', 3)
+    assert g.g_1.name is 'g_1'
+    assert g.g_2.name is 'g_2'
+    assert g.g_3.name is 'g_3'
+    g.remove_adjacent_node('g_3')
+    assert hasattr(g, 'g_3') is False
+    assert raises(ValueError, lambda: g.remove_adjacent_node('g_3'))
+    g.add_adjacent_node('g_1', 4)
+    assert g.g_1.data is 4
+    assert str(g) == "('g', 0)"
+
+def test_AdjacencyMatrixGraphNode():
+    g = AdjacencyMatrixGraphNode('g', 3)
+    assert str(g) == "('g', 3)"
+
+def test_GraphEdge():
+    g_1 = AdjacencyListGraphNode('g_1', 1)
+    g_2 = AdjacencyListGraphNode('g_2', 2)
+    e = GraphEdge(g_1, g_2, value=2)
+    assert str(e) == "('g_1', 'g_2')"