@@ -64,9 +64,9 @@ def uniform_hypergraph_Gnm(k: int, num_v: int, num_e: int):
 
 def hypergraph_Gnm(num_v: int, num_e: int, method:str="uniform", prob_k_list: Optional[List[float]] = None):
     r"""Return a random hypergraph with ``num_v`` vertices and ``num_e`` hyperedges. The ``method`` argument determines the distribution of the hyperedge degree.
-    The ``method`` can be one of ``"uniform"``, ``"low_order_first"``, ``"high_order_first"``. 
+    The ``method`` can be one of ``"uniform"``, ``"low_order_first"``, ``"high_order_first"``.
 
-    - If set to ``"uniform"``, the number of hyperedges with the same degree will approximately to the capacity of each hyperedge degree. 
+    - If set to ``"uniform"``, the number of hyperedges with the same degree will approximately to the capacity of each hyperedge degree.
       For example, the ``num_v`` is :math:`10`. The capacity of hyperedges with degree  :math:`2` is :math:`C^2_{10} = 45`.
     - If set to ``"low_order_first"``, the generated hyperedges will tend to have low degrees.
     - If set to ``"high_order_first"``, the generated hyperedges will tend to have high degrees.
@@ -90,10 +90,13 @@ def hypergraph_Gnm(num_v: int, num_e: int, method:str="uniform", prob_k_list: Op
     if method == "uniform":
         prob_k_list = [C(num_v, k) / (2 ** num_v - 1) for k in deg_e_list]
     elif method == "low_order_first":
-        # TODO
-        raise NotImplementedError
+        prob_k_list = [1.8 ** (-k) for k in deg_e_list]
+        sum_of_prob_k_list = sum(prob_k_list)
+        prob_k_list = [prob_k / sum_of_prob_k_list for prob_k in prob_k_list]
     elif method == "high_order_first":
-        raise NotImplementedError
+        prob_k_list = [1.8 ** (-k) for k in deg_e_list].reverse()
+        sum_of_prob_k_list = sum(prob_k_list)
+        prob_k_list = [prob_k / sum_of_prob_k_list for prob_k in prob_k_list]
     else:
         raise ValueError(f"Unknown method: {method}")
 
 
@@ -3,9 +3,95 @@ Structure Visualization
 
 Coming soon!
 
-.. Basic Usage
-.. --------------
-.. init a structure, call the draw method, and plt.show(), and plt.savefig().
+Basic Usage
+--------------
+DHG provides a simple interface to visualize the structures:
+
+1. Create a Structure object (*i.e.*, ``Graph``, ``BiGraph``, ``DiGraph``, and ``Hypergraph``);
+
+2. Call the ``draw`` method of the object;
+
+3. Call ``plt.show()`` to show the figure or ``plt.savefig()`` to save the figure.
+
+Visualization for ``Graph``
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. code-block:: python
+
+    import matplotlib.pyplot as plt
+    from dhg.random import graph_Gnm
+
+    g = graph_Gnm(100, 50)
+    g.draw()
+    plt.show()
+
+
+.. image:: ../_static/img/vis_graph.png
+    :align: center
+    :alt: vis_graph
+    :height: 200px
+
+
+Visualization for ``DiGraph``
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. code-block:: python
+
+    import matplotlib.pyplot as plt
+    from dhg.random import digraph_Gnm
+
+    g = digraph_Gnm(100, 50)
+    g.draw()
+    plt.show()
+
+
+.. image:: ../_static/img/vis_digraph.png
+    :align: center
+    :alt: vis_digraph
+    :height: 200px
+
+
+Visualization for ``BiGraph``
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+
+.. code-block:: python
+
+    import matplotlib.pyplot as plt
+    from dhg.random import bigraph_Gnm
+
+    g = bigraph_Gnm(100, 80, 20)
+    g.draw()
+    plt.show()
+
+
+.. image:: ../_static/img/vis_bigraph.png
+    :align: center
+    :alt: vis_bigraph
+    :height: 200px
+
+
+
+Visualization for ``Hypergraph``
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+
+.. code-block:: python
+
+    import matplotlib.pyplot as plt
+    from dhg.random import hypergraph_Gnm
+
+    h = hypergraph_Gnm(100, 10, method='low_order_first')
+    h.draw()
+    plt.show()
+
+
+.. image:: ../_static/img/vis_hypergraph.png
+    :align: center
+    :alt: vis_hypergraph
+    :height: 200px
+
+
 
 
 .. Advanced Usage
@@ -28,6 +114,3 @@ Coming soon!
 
 .. Simple Hypergraph
 .. ~~~~~~~~~~~~~~~~~~
-
-
-