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Determining if vertices lie within a set vertices

In my algorithm, I am finding graphs at different thresholds. Each graph G = (V,E). These are undirected graphs found using breadth first search. I would like to determine if the vertices of another graph G' = (V',E') lie within graph G. I am unfamiliar with graph algorithms so please let me know if you would like to see code or a more thorough explanation.
For example, If I have a graph G1 which is a square with 'corner' vertices (among others, but reduced for simplicity) of {(1,1), (1,6), (6,6), (6,1)}, then a smaller square G2 defined by corner vertices {(2,2), (2,5), (5,5), (5,2)} would lie within G1. The third graph G3 defined by corners {(3,3), (3,4), (4,4),(4,3)}. My algorithm produces the following figure for this configuration:
A square thresholded at 2, surrounded by t=1, surrounded by t=0. (I need to fix the edges but the vertices are correct)
My algorithm works on the following matrix:
import numpy as np
A = np.zeros((7,7))
#A[A<1] = -1
for i in np.arange(1,6):
for j in np.arange(1,6):
A[i,j] = 1
for i in np.arange(2,5):
for j in np.arange(2,5):
A[i,j] = 2
for i in np.arange(3,4):
for j in np.arange(3,4):
A[i,j] = 3
print(A)
To create three graphs, the first at threshold 2, the second at threshold 1, the third at threshold 0.
v1 = [[(3.0, 2.25), (3.0, 3.75), (2.25, 3.0), (3.75, 3.0)]]
v2 = [[(2.0, 1.333333), (1.333333, 3.0), (1.333333, 2.0), (1.333333, 4.0), (2.0, 4.666667), (3.0, 4.666667), (4.0, 4.666667), (4.666667, 4.0), (4.666667, 3.0), (4.666667, 2.0), (4.0, 1.333333), (3.0, 1.333333)]]
v3 = [[(1.0, 0.5), (0.5, 2.0), (0.5, 1.0), (0.5, 3.0), (0.5, 4.0), (0.5, 5.0), (1.0, 5.5), (2.0, 5.5), (3.0, 5.5), (4.0, 5.5), (5.0, 5.5), (5.5, 5.0), (5.5, 4.0), (5.5, 3.0), (5.5, 2.0), (5.5, 1.0), (5.0, 0.5), (4.0, 0.5), (3.0, 0.5), (2.0, 0.5)]]
And edge lists:
e1 = [[[2.25, 3.0], [3.0, 2.25]], [[3.0, 3.75], [2.25, 3.0]], [[3.0, 2.25], [3.75, 3.0]], [[3.0, 3.75], [3.75, 3.0]]]
e2 = [[[1.333333, 2.0], [2.0, 1.333333]], [[1.333333, 3.0], [1.333333, 2.0]], [[1.333333, 4.0], [1.333333, 3.0]], [[2.0, 4.666667], [1.333333, 4.0]], [[2.0, 1.333333], [3.0, 1.333333]], [[2.0, 4.666667], [3.0, 4.666667]], [[3.0, 1.333333], [4.0, 1.333333]], [[3.0, 4.666667], [4.0, 4.666667]], [[4.0, 1.333333], [4.666667, 2.0]], [[4.666667, 3.0], [4.666667, 2.0]], [[4.666667, 4.0], [4.666667, 3.0]], [[4.0, 4.666667], [4.666667, 4.0]]]
e3 = [[[0.5, 1.0], [1.0, 0.5]], [[0.5, 2.0], [0.5, 1.0]], [[0.5, 3.0], [0.5, 2.0]], [[0.5, 4.0], [0.5, 3.0]], [[0.5, 5.0], [0.5, 4.0]], [[1.0, 5.5], [0.5, 5.0]], [[1.0, 0.5], [2.0, 0.5]], [[1.0, 5.5], [2.0, 5.5]], [[2.0, 0.5], [3.0, 0.5]], [[2.0, 5.5], [3.0, 5.5]], [[3.0, 0.5], [4.0, 0.5]], [[3.0, 5.5], [4.0, 5.5]], [[4.0, 0.5], [5.0, 0.5]], [[4.0, 5.5], [5.0, 5.5]], [[5.0, 0.5], [5.5, 1.0]], [[5.5, 2.0], [5.5, 1.0]], [[5.5, 3.0], [5.5, 2.0]], [[5.5, 4.0], [5.5, 3.0]], [[5.5, 5.0], [5.5, 4.0]], [[5.0, 5.5], [5.5, 5.0]]]
Again, this gives graphs that look like this
This is the real data that I am working on. More complicated shapes.
Here, for example, I have a red shape inside of a green shape. Ideally, red shapes would lie within red shapes. They would be grouped together in one object (say an array of graphs).
The graphs are connected in a clockwise fashion. I really don't know how to describe it, but perhaps the graphs in the link show this. There's a bug on two of the lines (as you can see in the first plot, in the top right corner), but the vertices are correct.
Hope this helps! I can attach a full workable example, but it would include my whole algorithm and be pages long, with many functions! I basically want to use either input either g1, g2, and g3 into a function (or e1, e2, and e3). The function would tell me that g3 is contained with g2, which is contained within g1.

Your problem really does not have much to do with networks. Fundamentally, you are trying to determine if a point is inside a region described by an ordered list of points. The simplest way to this is to create matplotlib Path which has a contains_point method (there is also a 'contains_points` method to test many points simultaneously).
#!/usr/bin/env python
"""
Determine if a point is within the area defined by a path.
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.path import Path
from matplotlib.patches import PathPatch
point = [0.5, 0.5]
vertices = np.array([
[0, 0],
[0, 1],
[1, 1],
[1, 0],
[0, 0] # NOTE the repetition of the first vertex
])
path = Path(vertices, closed=True)
print(path.contains_point(point))
# True
# plot to check visually
fig, ax = plt.subplots(1,1)
ax.add_patch(PathPatch(path))
ax.plot(point[0], point[1], 'ro')
Note that if a point is directly on the path, it is not inside the path. However, contains_point supports a radius argument that allows you to add an increment to the extent of the area. Whether you need a positive or negative increment depends on the ordering of the points. IIRC, radius shifts the path left in direction of the path but don't quote me on that.

How to determine if one graph lies within another (vertices on a Cartesian grid)

In my algorithm, I am finding graphs at different thresholds. Each graph G = (V,E). These are undirected graphs found using breadth first search. I would like to determine if the vertices of another graph G' = (V',E') lie within graph G. I am unfamiliar with graph algorithms so please let me know if you would like to see code or a more thorough explanation.
For example, If I have a graph G which is a square with 'corner' vertices (among others, but reduced for simplicity) of (0,0), (0,8), (8,8), and (8,0), then the smaller square defined by corner vertices (2,2), (2,4), (4,4), and (4,2) would lie within G. I am sorry if this is an obvious question, I am just unfamiliar with working with graphs and could use a pointer or two (keywords welcome).
Edit:
My algorithm works on the following matrix:
import numpy as np
A = np.zeros((9,9))
for i in np.arange(1,8):
for j in np.arange(1,8):
A[i,j] = 1
for i in np.arange(2,4):
for j in np.arange(2,4):
A[i,j] = 2
print(A)
yields the matrix:
[[-1. -1. -1. -1. -1. -1. -1. -1. -1.]
[-1. 1. 1. 1. 1. 1. 1. 1. -1.]
[-1. 1. 2. 2. 1. 1. 1. 1. -1.]
[-1. 1. 2. 2. 1. 1. 1. 1. -1.]
[-1. 1. 1. 1. 1. 1. 1. 1. -1.]
[-1. 1. 1. 1. 1. 1. 1. 1. -1.]
[-1. 1. 1. 1. 1. 1. 1. 1. -1.]
[-1. 1. 1. 1. 1. 1. 1. 1. -1.]
[-1. -1. -1. -1. -1. -1. -1. -1. -1.]]
To create two graphs:
]
With vertices:
V1 = [[(2.0, 1.333333), (1.333333, 3.0), (1.333333, 2.0), (2.0, 3.666667), (3.0, 3.666667), (3.666667, 3.0), (3.666667, 2.0), (3.0, 1.333333)]]
V2 = [[(1.0, 0.5), (0.5, 2.0), (0.5, 1.0), (0.5, 3.0), (0.5, 4.0), (0.5, 5.0), (0.5, 6.0), (0.5, 7.0), (1.0, 7.5), (2.0, 7.5), (3.0, 7.5), (4.0, 7.5), (5.0, 7.5), (6.0, 7.5), (7.0, 7.5), (7.5, 7.0), (7.5, 6.0), (7.5, 5.0), (7.5, 4.0), (7.5, 3.0), (7.5, 2.0), (7.5, 1.0), (7.0, 0.5), (6.0, 0.5), (5.0, 0.5), (4.0, 0.5), (3.0, 0.5), (2.0, 0.5)]]
And edge lists:
e1 = [[[1.333333, 2.0], [2.0, 1.333333]], [[1.333333, 3.0], [1.333333, 2.0]], [[2.0, 3.666667], [1.333333, 3.0]], [[2.0, 1.333333], [3.0, 1.333333]], [[2.0, 3.666667], [3.0, 3.666667]], [[3.0, 1.333333], [3.666667, 2.0]], [[3.666667, 3.0], [3.666667, 2.0]], [[3.0, 3.666667], [3.666667, 3.0]]]
e2 = [[[0.5, 1.0], [1.0, 0.5]], [[0.5, 2.0], [0.5, 1.0]], [[0.5, 3.0], [0.5, 2.0]], [[0.5, 4.0], [0.5, 3.0]], [[0.5, 5.0], [0.5, 4.0]], [[0.5, 6.0], [0.5, 5.0]], [[0.5, 7.0], [0.5, 6.0]], [[1.0, 7.5], [0.5, 7.0]], [[1.0, 0.5], [2.0, 0.5]], [[1.0, 7.5], [2.0, 7.5]], [[2.0, 0.5], [3.0, 0.5]], [[2.0, 7.5], [3.0, 7.5]], [[3.0, 0.5], [4.0, 0.5]], [[3.0, 7.5], [4.0, 7.5]], [[4.0, 0.5], [5.0, 0.5]], [[4.0, 7.5], [5.0, 7.5]], [[5.0, 0.5], [6.0, 0.5]], [[5.0, 7.5], [6.0, 7.5]], [[6.0, 0.5], [7.0, 0.5]], [[6.0, 7.5], [7.0, 7.5]], [[7.0, 0.5], [7.5, 1.0]], [[7.5, 2.0], [7.5, 1.0]], [[7.5, 3.0], [7.5, 2.0]], [[7.5, 4.0], [7.5, 3.0]], [[7.5, 5.0], [7.5, 4.0]], [[7.5, 6.0], [7.5, 5.0]], [[7.5, 7.0], [7.5,
6.0]], [[7.0, 7.5], [7.5, 7.0]]]
I hope to use it on finding more complicated shapes like the following:
]
In the second picture, I have a red shape inside of a green shape. Ideally, red shapes would lie within red shapes.
I can attach a full workable example, but it would include my whole algorithm and be pages long, with many functions! I basically want to use either input (V1, E1) and (V2, E2) into a function, which would tell me whether one lies within the other.

You can use ray-casting to figure this out. It's a common method for dealing with this problem, so you can find additional information on it elsewhere too. The general description of the algorithm is this:
G1 and G2 are graphs whose edges form a simple polygon/convex hull, where we are attempting to determine if G2 is inside G1.
Choose some arbitrary direction in your space.
For each vertex in G2, cast a ray (a line that starts from one point and extends infinitely in a single direction) in the direction you chose.
If the vertex (a) intersects an edge of G1 an odd number of times OR (b) lies on one of those edges--> the vertex is inside of G1. For all other cases, the vertex is not inside of G1.
G2 is inside of G1 if an only if each vertex of G2 is inside of G1.
This will involve the following subtasks
-Get a list of vertices for G2
-Casting the rays
-Detecting and counting intersection
If you loop through each vertex and draw a line by adding the value you are using to represent G2 on your matrix to all cells in the direction you choose, the intersection value would then just be the sum of the values you are using to represent G1 and G2. In your current case, because you're making squares, this is a little problematic. There may be a better algorithm for drawing the objects or a better way to detect intersections.
Lastly, for detecting if en edge lies on the graph, you should run the check for intersections BEFORE you loop through the vertices. If any of your vertices produce the intersection value before the ray casting, it will tell you that it is on the edge of G1. Mark that this vertex is inside G1, remove it from the list of vertices that need to be checked, and make note of this value so it doesn't count as an extra intersection for all
You may have to tweak this algorithm depending on things like whether you want to count nodes on the edge as inside or outside, or whether you need all vertices inside the figure, but I hope this is a helpful start.

Confusing result for panda qcut function

When reading the documentation for pd.qcut?, I simply couldn't understand its writing, particularly with its examples, one of them is below
>>> pd.qcut(range(5), 4)
... # doctest: +ELLIPSIS
[(-0.001, 1.0], (-0.001, 1.0], (1.0, 2.0], (2.0, 3.0], (3.0, 4.0]]
Categories (4, interval[float64]): [(-0.001, 1.0] < (1.0, 2.0] ...
Why did it return 5 elements in the list (although the code specifying 4 buckets) and the 2 first elements are the same (-0.001, 1.0)?
Thanks.

Because 0 is in (-0.001, 1], so is 1.
range(5) # [0, 1, 2, 3, 4, 5]
The corresponding category of [0, 1, 2, 3, 4, 5] is [(-0.001, 1.0], (-0.001, 1.0], (1.0, 2.0], (2.0, 3.0], (3.0, 4.0]].

Look at the range
list(range(5))
Out[116]: [0, 1, 2, 3, 4]
it is return 5 number , when you do qcut , 0,1 are considered into one range
pd.qcut(range(5), 4)
Out[115]:
[(-0.001, 1.0], (-0.001, 1.0], (1.0, 2.0], (2.0, 3.0], (3.0, 4.0]]
Categories (4, interval[float64]): [(-0.001, 1.0] < (1.0, 2.0] < (2.0, 3.0] < (3.0, 4.0]]

Convert an array stored as a string, to a proper numpy array

For long and tedious reasons, I have lots of arrays that are stored as strings:
tmp = '[[1.0, 3.0, 0.4]\n [3.0, 4.0, -1.0]\n [3.0, 4.0, 0.1]\n [3.0, 4.0, 0.2]]'
Now I obviously do not want my arrays as long strings, I want them as proper numpy arrays so I can use them. Consequently, what is a good way to convert the above to:
tmp_np = np.array([[1.0, 3.0, 0.4]
[3.0, 4.0, -1.0]
[3.0, 4.0, 0.1]
[3.0, 4.0, 0.2]])
such that I can do simple things like tmp_np.shape = (4,3) or simple indexing tmp_np[0,:] = [1.0, 3.0, 0.4] etc.
Thanks

You can use ast.literal_eval, if you replace your \n characters with ,:
temp_np = np.array(ast.literal_eval(tmp.replace('\n', ',')))
Returns:
>>> tmp_np
array([[ 1. , 3. , 0.4],
[ 3. , 4. , -1. ],
[ 3. , 4. , 0.1],
[ 3. , 4. , 0.2]])

np.array returning numpy.ndarray with "..."

I created a script to generate a list:
import random
nota1 = range (5, 11)
nota2 = range (5, 11)
nota3 = range (5, 11)
nota4 = range (0, 2)
dados = []
for i in range(1000):
dados_dado = []
n1 = random.choice(nota1)
n2 = random.choice(nota2)
n3 = random.choice(nota3)
n4 = random.choice(nota4)
n1 = float (n1)
n2 = float (n2)
n3 = float (n3)
n4 = float (n4)
dados_dado.append (n1)
dados_dado.append (n2)
dados_dado.append (n3)
dados_dado.append (n4)
dados.append (dados_dado)
When i print type (dados) python return: <type 'list'>, a huge list that looks like this:
[[5.0, 8.0, 10.0, 1.0], [8.0, 9.0, 9.0, 1.0], [7.0, 5.0, 6.0, 1.0], [5.0, 8.0, 7.0, 0.0], [9.0, 7.0, 10.0, 0.0], [6.0, 7.0, 9.0, 1.0], [6.0, 9.0, 8.0, 1.0]]
I need to transform it to <type 'numpy.ndarray'> so i made :
data = np.array(dados)
What i expected to return was something like this:
[[ 6.8 3.2 5.9 2.3]
[ 6.7 3.3 5.7 2.5]
[ 6.7 3. 5.2 2.3]
[ 6.3 2.5 5. 1.9]
[ 6.5 3. 5.2 2. ]
[ 6.2 3.4 5.4 2.3]
[ 5.9 3. 5.1 1.8]]
But, what i get instead is:
[[ 7. 10. 6. 1.]
[ 8. 6. 6. 1.]
[ 6. 9. 5. 0.]
...,
[ 9. 7. 10. 0.]
[ 6. 7. 9. 1.]
[ 6. 9. 8. 1.]]
What am i doing wrong?

With your sample:
In [574]: dados=[[5.0, 8.0, 10.0, 1.0], [8.0, 9.0, 9.0, 1.0], [7.0, 5.0, 6.0, 1.
...: 0], [5.0, 8.0, 7.0, 0.0], [9.0, 7.0, 10.0, 0.0], [6.0, 7.0, 9.0, 1.0],
...: [6.0, 9.0, 8.0, 1.0]]
In [575]: print(dados)
[[5.0, 8.0, 10.0, 1.0], [8.0, 9.0, 9.0, 1.0], [7.0, 5.0, 6.0, 1.0], [5.0, 8.0, 7.0, 0.0], [9.0, 7.0, 10.0, 0.0], [6.0, 7.0, 9.0, 1.0], [6.0, 9.0, 8.0, 1.0]]
convert it to an array, an see the whole thing. Your input didn't have decimals to numpy display omits those.
In [576]: print(np.array(dados))
[[ 5. 8. 10. 1.]
[ 8. 9. 9. 1.]
[ 7. 5. 6. 1.]
[ 5. 8. 7. 0.]
[ 9. 7. 10. 0.]
[ 6. 7. 9. 1.]
[ 6. 9. 8. 1.]]
Replicate the list many times, and print display has this ..., rather than show 10,000 lines. That's nice isn't it?
In [577]: print(np.array(dados*1000))
[[ 5. 8. 10. 1.]
[ 8. 9. 9. 1.]
[ 7. 5. 6. 1.]
...,
[ 9. 7. 10. 0.]
[ 6. 7. 9. 1.]
[ 6. 9. 8. 1.]]
The full array is still there
In [578]: np.array(dados*1000).shape
Out[578]: (7000, 4)
The default is for numpy to add the ellipsis when the total number of entries is 1000. Do you really need to see all those lines?
That print standard can be changed, but I question whether you need to do that.

Your array is fine. NumPy just suppresses display of the whole array for large arrays by default.
(If you actually were expecting your array to be short enough not to trigger this behavior, or if you were actually expecting it to have non-integer entries, you'll have to explain why you expected that.)

numpy.set_printoptions(precision=20)
Will give you more displayabilty, set precision as you desire.