diff --git a/README.md b/README.md
index 75353bb..d86ca94 100644
--- a/README.md
+++ b/README.md
@@ -184,6 +184,13 @@ structure which preserve and reuse previous versions. This uses a very
 functional, cons-style of list manipulation. Insert, get, remove, and size
 operations are O(n) as you would expect.
 
+#### Simple Graph
+
+A mutable, non-persistent undirected graph where parallel edges and self-loops are 
+not permitted. Operations to add an edge as well as retrieve the total number of 
+vertices/edges are O(1) while the operation to retrieve the vertices adjacent to a
+target is O(n). For more details see [wikipedia](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)#Simple_graph)
+
 ### Installation
 
  1. Install Go 1.3 or higher.
diff --git a/graph/simple.go b/graph/simple.go
new file mode 100644
index 0000000..b01a1e3
--- /dev/null
+++ b/graph/simple.go
@@ -0,0 +1,136 @@
+/*
+Copyright 2017 Julian Griggs
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Package graph provides graph implementations. Currently, this includes an
+undirected simple graph.
+*/
+package graph
+
+import (
+	"errors"
+	"sync"
+)
+
+var (
+	// ErrVertexNotFound is returned when an operation is requested on a
+	// non-existent vertex.
+	ErrVertexNotFound = errors.New("vertex not found")
+
+	// ErrSelfLoop is returned when an operation tries to create a disallowed
+	// self loop.
+	ErrSelfLoop = errors.New("self loops not permitted")
+
+	// ErrParallelEdge is returned when an operation tries to create a
+	// disallowed parallel edge.
+	ErrParallelEdge = errors.New("parallel edges are not permitted")
+)
+
+// SimpleGraph is a mutable, non-persistent undirected graph.
+// Parallel edges and self-loops are not permitted.
+// Additional description: https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)#Simple_graph
+type SimpleGraph struct {
+	mutex         sync.RWMutex
+	adjacencyList map[interface{}]map[interface{}]struct{}
+	v, e          int
+}
+
+// V returns the number of vertices in the SimpleGraph
+func (g *SimpleGraph) V() int {
+	g.mutex.RLock()
+	defer g.mutex.RUnlock()
+
+	return g.v
+}
+
+// E returns the number of edges in the SimpleGraph
+func (g *SimpleGraph) E() int {
+	g.mutex.RLock()
+	defer g.mutex.RUnlock()
+
+	return g.e
+}
+
+// AddEdge will create an edge between vertices v and w
+func (g *SimpleGraph) AddEdge(v, w interface{}) error {
+	g.mutex.Lock()
+	defer g.mutex.Unlock()
+
+	if v == w {
+		return ErrSelfLoop
+	}
+
+	g.addVertex(v)
+	g.addVertex(w)
+
+	if _, ok := g.adjacencyList[v][w]; ok {
+		return ErrParallelEdge
+	}
+
+	g.adjacencyList[v][w] = struct{}{}
+	g.adjacencyList[w][v] = struct{}{}
+	g.e++
+	return nil
+}
+
+// Adj returns the list of all vertices connected to v
+func (g *SimpleGraph) Adj(v interface{}) ([]interface{}, error) {
+	g.mutex.RLock()
+	defer g.mutex.RUnlock()
+
+	deg, err := g.Degree(v)
+	if err != nil {
+		return nil, ErrVertexNotFound
+	}
+
+	adj := make([]interface{}, deg)
+	i := 0
+	for key := range g.adjacencyList[v] {
+		adj[i] = key
+		i++
+	}
+	return adj, nil
+}
+
+// Degree returns the number of vertices connected to v
+func (g *SimpleGraph) Degree(v interface{}) (int, error) {
+	g.mutex.RLock()
+	defer g.mutex.RUnlock()
+
+	val, ok := g.adjacencyList[v]
+	if !ok {
+		return 0, ErrVertexNotFound
+	}
+	return len(val), nil
+}
+
+func (g *SimpleGraph) addVertex(v interface{}) {
+	mm, ok := g.adjacencyList[v]
+	if !ok {
+		mm = make(map[interface{}]struct{})
+		g.adjacencyList[v] = mm
+		g.v++
+	}
+}
+
+// NewSimpleGraph creates and returns a SimpleGraph
+func NewSimpleGraph() *SimpleGraph {
+	return &SimpleGraph{
+		adjacencyList: make(map[interface{}]map[interface{}]struct{}),
+		v:             0,
+		e:             0,
+	}
+}
diff --git a/graph/simple_test.go b/graph/simple_test.go
new file mode 100644
index 0000000..9a0edbc
--- /dev/null
+++ b/graph/simple_test.go
@@ -0,0 +1,246 @@
+/*
+Copyright 2017 Julian Griggs
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+package graph
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestV(t *testing.T) {
+	assert := assert.New(t)
+	sgraph := NewSimpleGraph()
+	assert.Equal(0, sgraph.V())
+
+	sgraph.AddEdge("A", "B")
+	assert.Equal(2, sgraph.V())
+
+	sgraph.AddEdge("B", "C")
+	assert.Equal(3, sgraph.V())
+
+	sgraph.AddEdge("A", "C")
+	assert.Equal(3, sgraph.V())
+
+	// Parallel edges not allowed
+	sgraph.AddEdge("A", "C")
+	assert.Equal(3, sgraph.V())
+	sgraph.AddEdge("C", "A")
+	assert.Equal(3, sgraph.V())
+
+	// Self loops not allowed
+	sgraph.AddEdge("C", "C")
+	assert.Equal(3, sgraph.V())
+	sgraph.AddEdge("D", "D")
+	assert.Equal(3, sgraph.V())
+}
+
+func TestE(t *testing.T) {
+	assert := assert.New(t)
+	sgraph := NewSimpleGraph()
+
+	assert.Equal(0, sgraph.E())
+
+	sgraph.AddEdge("A", "B")
+	assert.Equal(1, sgraph.E())
+
+	sgraph.AddEdge("B", "C")
+	assert.Equal(2, sgraph.E())
+
+	sgraph.AddEdge("A", "C")
+	assert.Equal(3, sgraph.E())
+
+	// Parallel edges not allowed
+	sgraph.AddEdge("A", "C")
+	assert.Equal(3, sgraph.E())
+	sgraph.AddEdge("C", "A")
+	assert.Equal(3, sgraph.E())
+
+	// Self loops not allowed so no edges added
+	sgraph.AddEdge("C", "C")
+	assert.Equal(3, sgraph.E())
+	sgraph.AddEdge("D", "D")
+	assert.Equal(3, sgraph.E())
+}
+
+func TestDegree(t *testing.T) {
+	assert := assert.New(t)
+	sgraph := NewSimpleGraph()
+
+	// No edges added so degree is 0
+	v, err := sgraph.Degree("A")
+	assert.Zero(v)
+	assert.Error(err)
+
+	// One edge added
+	sgraph.AddEdge("A", "B")
+	v, err = sgraph.Degree("A")
+	assert.Equal(1, v)
+	assert.Nil(err)
+
+	// Self loops are not allowed
+	sgraph.AddEdge("A", "A")
+	v, err = sgraph.Degree("A")
+	assert.Equal(1, v)
+	assert.Nil(err)
+
+	// Parallel edges are not allowed
+	sgraph.AddEdge("A", "B")
+	v, err = sgraph.Degree("A")
+	assert.Equal(1, v)
+	assert.Nil(err)
+	sgraph.AddEdge("B", "A")
+	v, err = sgraph.Degree("A")
+	assert.Equal(1, v)
+	assert.Nil(err)
+
+	v, err = sgraph.Degree("B")
+	assert.Equal(1, v)
+	assert.Nil(err)
+
+	sgraph.AddEdge("C", "D")
+	sgraph.AddEdge("A", "C")
+	sgraph.AddEdge("E", "F")
+	sgraph.AddEdge("E", "G")
+	sgraph.AddEdge("H", "G")
+
+	v, err = sgraph.Degree("A")
+	assert.Equal(2, v)
+	assert.Nil(err)
+
+	v, err = sgraph.Degree("B")
+	assert.Equal(1, v)
+	assert.Nil(err)
+
+	v, err = sgraph.Degree("C")
+	assert.Equal(2, v)
+	assert.Nil(err)
+
+	v, err = sgraph.Degree("D")
+	assert.Equal(1, v)
+	assert.Nil(err)
+
+	v, err = sgraph.Degree("E")
+	assert.Equal(2, v)
+	assert.Nil(err)
+
+	v, err = sgraph.Degree("G")
+	assert.Equal(2, v)
+	assert.Nil(err)
+}
+
+func TestAddEdge(t *testing.T) {
+	assert := assert.New(t)
+	sgraph := NewSimpleGraph()
+
+	err := sgraph.AddEdge("A", "B")
+	assert.Nil(err)
+
+	err = sgraph.AddEdge("A", "B")
+	assert.Error(err)
+
+	err = sgraph.AddEdge("B", "A")
+	assert.Error(err)
+
+	err = sgraph.AddEdge("A", "A")
+	assert.Error(err)
+
+	err = sgraph.AddEdge("C", "C")
+	assert.Error(err)
+
+	err = sgraph.AddEdge("B", "C")
+	assert.Nil(err)
+
+}
+
+func TestAdj(t *testing.T) {
+	assert := assert.New(t)
+	sgraph := NewSimpleGraph()
+
+	v, err := sgraph.Adj("A")
+	assert.Zero(v)
+	assert.Error(err)
+
+	// Self loops not allowed
+	sgraph.AddEdge("A", "A")
+	v, err = sgraph.Adj("A")
+	assert.Zero(v)
+	assert.Error(err)
+
+	sgraph.AddEdge("A", "B")
+	v, err = sgraph.Adj("A")
+	assert.Equal(1, len(v))
+	assert.Nil(err)
+	assert.Equal("B", v[0])
+
+	v, err = sgraph.Adj("B")
+	assert.Equal(1, len(v))
+	assert.Nil(err)
+	assert.Equal("A", v[0])
+
+	// Parallel Edges not allowed
+	sgraph.AddEdge("A", "B")
+	sgraph.AddEdge("B", "A")
+	v, err = sgraph.Adj("B")
+	assert.Equal(1, len(v))
+	assert.Nil(err)
+	assert.Equal("A", v[0])
+
+	sgraph.AddEdge("C", "D")
+	sgraph.AddEdge("A", "C")
+	sgraph.AddEdge("E", "F")
+	sgraph.AddEdge("E", "G")
+	sgraph.AddEdge("H", "G")
+
+	v, err = sgraph.Adj("A")
+	assert.Equal(2, len(v))
+	assert.Nil(err)
+	assert.Contains(v, "B")
+	assert.Contains(v, "C")
+	assert.NotContains(v, "A")
+	assert.NotContains(v, "D")
+
+	v, err = sgraph.Adj("B")
+	assert.Equal(1, len(v))
+	assert.Nil(err)
+	assert.Contains(v, "A")
+	assert.NotContains(v, "B")
+	assert.NotContains(v, "C")
+	assert.NotContains(v, "D")
+
+	v, err = sgraph.Adj("C")
+	assert.Equal(2, len(v))
+	assert.Nil(err)
+	assert.Contains(v, "A")
+	assert.Contains(v, "D")
+	assert.NotContains(v, "B")
+	assert.NotContains(v, "C")
+
+	v, err = sgraph.Adj("E")
+	assert.Equal(2, len(v))
+	assert.Nil(err)
+	assert.Contains(v, "F")
+	assert.Contains(v, "G")
+	assert.NotContains(v, "A")
+
+	v, err = sgraph.Adj("G")
+	assert.Equal(2, len(v))
+	assert.Nil(err)
+	assert.Contains(v, "E")
+	assert.Contains(v, "H")
+	assert.NotContains(v, "A")
+}