diff --git a/cz_table.py b/cz_table.py
deleted file mode 100644
index 882c8c9..0000000
--- a/cz_table.py
+++ /dev/null
@@ -1,14 +0,0 @@
-""" This part computes the CZ table """
-
-from util import cache_to_disk
-import qi
-import numpy as np
-from tqdm import tqdm
-import clifford
-
-#@cache_to_disk("cz_table.pkl")
-def construct_table():
-    print "awd"
-    return "awd"
-
-cz_table = construct_table()
diff --git a/graph.py b/graph.py
index f0800dd..3b4aaeb 100644
--- a/graph.py
+++ b/graph.py
@@ -4,68 +4,75 @@ Provides an extremely basic graph structure, based on neighbour lists
 
 from collections import defaultdict
 import itertools as it
-import clifford
-
-def graph():
-    """ Generate a graph with Hadamards on each qubit """
-    #return defaultdict(set), defaultdict(lambda: clifford.by_name["hadamard"])
-    return [set() for i in range(100)], [clifford.by_name["hadamard"] for i in range(100)]
-
-
-def add_edge(graph, v1, v2):
-    """ Add an edge between two vertices in the graph """
-    graph[v1].add(v2)
-    graph[v2].add(v1)
-
-def del_edge(graph, v1, v2):
-    """ Delete an edge between two vertices in the graph """
-    graph[v1].remove(v2)
-    graph[v2].remove(v1)
-
-def has_edge(graph, v1, v2):
-    """ Test existence of an edge between two vertices in the graph """
-    return v2 in graph[v1]
-
-def toggle_edge(graph, v1, v2):
-    """ Toggle an edge between two vertices in the graph """
-    if has_edge(graph, v1, v2):
-        del_edge(graph, v1, v2)
-    else:
-        add_edge(graph, v1, v2)
-
-def edgelist(g):
-    """ Describe a graph as an edgelist """
-    edges = frozenset(frozenset((i, n))
-            for i, v in enumerate(g)
-            for n in v)
-    return [tuple(e) for e in edges]
-
-def cphase(g, vops, a, b):
-    """ Act a controlled-phase gate on two qubits """
-    if g[a]-{b}: remove_vop(g, vops, a, b)
-    if g[b]-{a}: remove_vop(g, vops, b, a)
-    if g[a]-{b}: remove_vop(g, vops, a, b)
-    edge = has_edge(g, a, b)
-    new_edge, vops[a], vops[b] = cphase_table[edge, vops[a], vops[b]]
-    if new_edge != edge:
-        toggle_edge(g, a, b)
-    
-
-def remove_vop(g, vops, a, avoid):
-    """ Reduces VOP[a] to the identity, avoiding (if possible) the use of vertex b as a swapping partner """
-    others = g[a] - {avoid}
-    swap_qubit = others.pop() if others else avoid
-    for v in reversed(clifford.decompositions[vops[a]]):
-        local_complementation(g, vops, a if v == "x" else swap_qubit)
-
-
-def local_complementation(g, vops, v):
-    """ As defined in LISTING 1 of Anders & Briegel """
-    for i, j in it.combinations(g[v], 2):
-        toggle_edge(g, i, j)
-
-    # Update VOPs
-    vops[v] = clifford.times_table[vops[v]][clifford.by_name["sqx"]]
-    for i in g[v]:
-        vops[i] = clifford.times_table[vops[i]][clifford.by_name["msqz"]]
+import tables as clifford
+
+
+class GraphState(object):
+    def __init__(self):
+        self.ngbh = defaultdict(set)
+        self.vops = defaultdict(int)
+
+
+    def add_edge(self, v1, v2):
+        """ Add an edge between two vertices in the self """
+        if not v1 in self.ngbh: self.vops[v1] = clifford.by_name["hadamard"]
+        if not v2 in self.ngbh: self.vops[v2] = clifford.by_name["hadamard"]
+        self.ngbh[v1].add(v2)
+        self.ngbh[v2].add(v1)
+
+
+    def del_edge(self, v1, v2):
+        """ Delete an edge between two vertices in the self """
+        self.ngbh[v1].remove(v2)
+        self.ngbh[v2].remove(v1)
+
+
+    def has_edge(self, v1, v2):
+        """ Test existence of an edge between two vertices in the self """
+        return v2 in self.ngbh[v1]
+
+
+    def toggle_edge(self, v1, v2):
+        """ Toggle an edge between two vertices in the self """
+        if self.has_edge(v1, v2):
+            self.del_edge(v1, v2)
+        else:
+            self.add_edge(v1, v2)
+
+    def edgelist(self):
+        """ Describe a graph as an edgelist """
+        edges = frozenset(frozenset((i, n))
+                          for i, v in enumerate(self.ngbh.values())
+                          for n in v)
+        return [tuple(e) for e in edges]
+
+    def remove_vop(self, a, avoid):
+        """ Reduces VOP[a] to the identity, avoiding (if possible) the use of vertex b as a swapping partner """
+        others = self.ngbh[a] - {avoid}
+        swap_qubit = others.pop() if others else avoid
+        for v in reversed(clifford.decompositions[self.vops[a]]):
+            self.local_complementation(a if v == "x" else swap_qubit)
+
+    def cphase(self, a, b):
+        """ Act a controlled-phase gate on two qubits """
+        if self.ngbh[a] - {b}:
+            self.remove_vop(a, b)
+        if self.ngbh[b] - {a}:
+            self.remove_vop(b, a)
+        if self.ngbh[a] - {b}:
+            self.remove_vop(a, b)
+        edge = self.has_edge(a, b)
+        new_edge, vops[a], vops[b] = cphase_table[edge, vops[a], vops[b]]
+        if new_edge != edge:
+            self.toggle_edge(a, b)
+
+    def local_complementation(self, v):
+        """ As defined in LISTING 1 of Anders & Briegel """
+        for i, j in it.combinations(self.ngbh[v], 2):
+            self.toggle_edge(i, j)
+
+        # Update VOPs
+        self.vops[v] = clifford.times_table[self.vops[v]][clifford.by_name["sqx"]]
+        for i in self.ngbh[v]:
+            self.vops[i] = clifford.times_table[self.vops[i]][clifford.by_name["msqz"]]
 
diff --git a/clifford.py b/tables.py
similarity index 71%
rename from clifford.py
rename to tables.py
index ef3ed8a..9dc8008 100644
--- a/clifford.py
+++ b/tables.py
@@ -9,7 +9,21 @@ import numpy as np
 from tqdm import tqdm
 import qi
 from functools import reduce
-from util import cache_to_disk
+import cPickle
+
+def cache_to_disk(file_name):
+    """ A decorator to cache the output of a function to disk """
+    def wrap(func):
+        def modified(*args, **kwargs):
+            try:
+                output = cPickle.load(open(file_name, "r"))
+            except (IOError, ValueError):
+                output = func(*args, **kwargs)
+                with open(file_name, "w") as f:
+                    cPickle.dump(output, f)
+            return output
+        return modified
+    return wrap
 
 
 # TODO: make this more efficient / shorter
@@ -27,12 +41,13 @@ def compose_u(decomposition):
     us = (elements[c] for c in decomposition)
     return np.matrix(reduce(np.dot, us), dtype=complex)
 
+
 def name_of(vop):
     """ Get the formatted name of a VOP """
     return "%s" % get_name[vop] if vop in get_name else "VOP%d" % vop
 
 
-@cache_to_disk("clifford_tables.pkl")
+@cache_to_disk("tables.cache")
 def construct_tables():
     """ Constructs / caches multiplication and conjugation tables """
     by_name = {name: find_up_to_phase(u)[0] for name, u in qi.by_name.items()}
@@ -41,13 +56,14 @@ def construct_tables():
                          for i, u in enumerate(unitaries)]
     times_table = [[find_up_to_phase(u * v)[0] for v in unitaries]
                    for u in tqdm(unitaries)]
-    return by_name, get_name, conjugation_table, times_table
+    cz_table = None
+    return by_name, get_name, conjugation_table, times_table, cz_table
+
 
-# Various useful tables
 decompositions = ("xxxx", "xx", "zzxx", "zz", "zxx", "z", "zzz", "xxz",
      "xzx", "xzxxx", "xzzzx", "xxxzx", "xzz", "zzx", "xxx", "x",
      "zzzx", "xxzx", "zx", "zxxx", "xxxz", "xzzz", "xz", "xzxx")
 elements = {"x": qi.sqx, "z": qi.msqz}
 unitaries = [compose_u(d) for d in decompositions]
-by_name, get_name, conjugation_table, times_table = construct_tables()
+by_name, get_name, conjugation_table, times_table, cz_table = construct_tables()
 
diff --git a/tests/test_clifford.py b/tests/test_clifford.py
index cfc16f8..5df3ec5 100644
--- a/tests/test_clifford.py
+++ b/tests/test_clifford.py
@@ -1,4 +1,4 @@
-import clifford as lc
+import tables as lc
 from numpy import *
 from scipy.linalg import sqrtm
 import qi
diff --git a/tests/test_graph.py b/tests/test_graph.py
index 0ebc23a..d6eeacb 100644
--- a/tests/test_graph.py
+++ b/tests/test_graph.py
@@ -1,51 +1,52 @@
-from graph import *
+from graph import GraphState
+import tables as lc
 
 def test_graph():
-    g, v = graph()
-    add_edge(g, 0,1)
-    add_edge(g, 1,2)
-    add_edge(g, 2,0)
-    assert g[0]==set([1,2])
+    g = GraphState()
+    g.add_edge(0,1)
+    g.add_edge(1,2)
+    g.add_edge(2,0)
+    assert g.ngbh[0]==set([1,2])
 
-    del_edge(g, 0,1)
-    assert g[0]==set([2])
-    el = edgelist(g)
+    g.del_edge(0,1)
+    assert g.ngbh[0]==set([2])
+    el = g.edgelist()
     assert (1,2) in el
     assert not (0,1) in el
     assert len(el)==2
 
-    assert has_edge(g, 1,2)
-    assert not has_edge(g, 0,1)
+    assert g.has_edge(1,2)
+    assert not g.has_edge(0,1)
 
 def test_local_complementation():
     """ Test that local complementation works as expected """
-    g, vops = graph()
-    add_edge(g, 0, 1)
-    add_edge(g, 0, 2)
-    add_edge(g, 1, 2)
-    add_edge(g, 0, 3)
-    local_complementation(g, vops, 0)
-    assert has_edge(g, 0, 1)
-    assert has_edge(g, 0, 2)
-    assert not has_edge(g, 1, 2)
-    assert has_edge(g, 3, 2)
-    assert has_edge(g, 3, 1)
+    g = GraphState()
+    g.add_edge(0,1)
+    g.add_edge(1,2)
+    g.add_edge(2,0)
+    g.add_edge(0,3)
+    g.local_complementation(0)
+    assert g.has_edge(0, 1)
+    assert g.has_edge(0, 2)
+    assert not g.has_edge(1, 2)
+    assert g.has_edge(3, 2)
+    assert g.has_edge(3, 1)
 
     # TODO: test VOP conditions
 
 def test_remove_vop():
     """ Test that removing VOPs really works """
-    g, vops = graph()
-    add_edge(g, 0, 1)
-    add_edge(g, 0, 2)
-    add_edge(g, 1, 2)
-    add_edge(g, 0, 3)
-    remove_vop(g, vops, 0, 1)
-    assert vops[0] == clifford.by_name["identity"]
-    remove_vop(g, vops, 1, 1)
-    assert vops[1] == clifford.by_name["identity"]
-    remove_vop(g, vops, 2, 1)
-    assert vops[2] == clifford.by_name["identity"]
-    remove_vop(g, vops, 0, 1)
-    assert vops[0] == clifford.by_name["identity"]
+    g = GraphState()
+    g.add_edge(0,1)
+    g.add_edge(1,2)
+    g.add_edge(2,0)
+    g.add_edge(0,3)
+    g.remove_vop(0, 1)
+    assert g.vops[0] == lc.by_name["identity"]
+    g.remove_vop(1, 1)
+    assert g.vops[1] == lc.by_name["identity"]
+    g.remove_vop(2, 1)
+    assert g.vops[2] == lc.by_name["identity"]
+    g.remove_vop(0, 1)
+    assert g.vops[0] == lc.by_name["identity"]
 
diff --git a/tests/test_viz.py b/tests/test_viz.py
new file mode 100644
index 0000000..e15d8f5
--- /dev/null
+++ b/tests/test_viz.py
@@ -0,0 +1,11 @@
+from graph import GraphState
+import viz
+
+def test_viz():
+    g = GraphState()
+    g.add_edge(0,1)
+    g.add_edge(1,2)
+    g.add_edge(2,0)
+    g.add_edge(0,3)
+    print g.vops
+    viz.draw(g)
diff --git a/util.py b/util.py
index 810fb53..0e66ebf 100644
--- a/util.py
+++ b/util.py
@@ -1,14 +1,7 @@
 """ 
 Useful but messy crap
 """
-import cPickle
-import networkx as nx
-from matplotlib import pyplot as plt
-from graph import *
-import clifford
-import numpy as np
 
-VOP_COLORS = ["red", "green", "blue", "orange", "yellow", "purple", "black", "white"]
 
 def cache_to_disk(file_name):
     """ A decorator to cache the output of a function to disk """
@@ -25,21 +18,3 @@ def cache_to_disk(file_name):
     return wrap
 
 
-def draw(graph, vops, filename="out.pdf", pos=None, ns=500):
-    """ Draw a graph with networkx layout """
-    plt.clf()
-    g = nx.from_edgelist(edgelist(graph))
-    pos = nx.spring_layout(g) if pos==None else pos
-    colors = [VOP_COLORS[vop % len(VOP_COLORS)] for vop in vops]
-    nx.draw_networkx_nodes(g, pos, node_color="white", node_size=ns)
-    nx.draw_networkx_nodes(g, pos, node_color=colors, node_size=ns, alpha=.4)
-    nx.draw_networkx_edges(g, pos, edge_color="gray")
-    nx.draw_networkx_labels(g, pos, font_family="FreeSans")
-
-    labels = {i: clifford.name_of(vops[i]) for i in g.nodes()}
-    pos = {k: v + np.array([0, -.1]) for k, v in pos.items()}
-    nx.draw_networkx_labels(g, pos, labels, font_family="FreeSans")
-    plt.axis('off')
-    plt.savefig(filename)
-    return pos
-
diff --git a/viz.py b/viz.py
new file mode 100644
index 0000000..fe1d632
--- /dev/null
+++ b/viz.py
@@ -0,0 +1,25 @@
+import networkx as nx
+from matplotlib import pyplot as plt
+import tables
+import numpy as np
+from graph import GraphState
+
+VOP_COLORS = ["red", "green", "blue", "orange", "yellow", "purple", "black", "white"]
+
+def draw(state, filename="out.pdf", pos=None, ns=500):
+    """ Draw a graph with networkx layout """
+    plt.clf()
+    graph = nx.from_edgelist(state.edgelist())
+    pos = nx.spring_layout(graph) if pos==None else pos
+    colors = [VOP_COLORS[vop % len(VOP_COLORS)] for vop in state.vops.values()]
+    nx.draw_networkx_nodes(graph, pos, node_color="white", node_size=ns)
+    nx.draw_networkx_nodes(graph, pos, node_color=colors, node_size=ns, alpha=.4)
+    nx.draw_networkx_edges(graph, pos, edge_color="gray")
+    nx.draw_networkx_labels(graph, pos, font_family="FreeSans")
+
+    labels = {i: tables.name_of(v) for i, v in state.vops.items()}
+    pos = {k: v + np.array([0, -.1]) for k, v in pos.items()}
+    nx.draw_networkx_labels(graph, pos, labels, font_family="FreeSans")
+    plt.axis('off')
+    plt.savefig(filename)
+    return pos