# Get the most out of CausalNex plotting¶

The goal of this tutorial is to help you build pretty and meaningful plots from CausalNex networks. We will help you customise your graph for your specific application, whether you seek a specific trend in the network or you wish to use the plotting in a presentation or article.

We will go through the following items:

• Explore customisations available in CausalNex:

• A huge number of customisations is possible, which can make the existent documentation overwhelming.

• With examples, we show the main customisations available, and give tips of meaningful choices.

• Understand Graphviz, the engine used in CausalNex visualisations:

• CausalNex renders visualisation by interacting with a software called Graphviz.

• We explain the basics of this software and how this interaction takes place.

• Explore alternative solutions:

• We exemplify how to use networkx for plotting. This may be a friendly alternative, as it uses matplotlib to render the images.

## Explore customisations available in CausalNex¶

In this tutorial, we work with following Bayesian Network structure, known as “Insurance network”. This network was first introduced in 1.

Note that we create random weights for each edges. These could mean, in a real model, any indication of the edge strength, such as the weights output by NOTEARS.

[2]:

import numpy as np
from causalnex.structure import StructureModel
from causalnex.plots import plot_structure
from IPython.display import Image

import warnings

warnings.filterwarnings("ignore")

from itertools import chain

edges = [
("Age", "SocioEcon", {"weight": 0.37}),
("SocioEcon", "OtherCar", {"weight": 0.95}),
("SocioEcon", "GoodStudent", {"weight": 0.73}),
("Age", "GoodStudent", {"weight": 0.6}),
("SocioEcon", "RiskAversion", {"weight": 0.16}),
("Age", "RiskAversion", {"weight": 0.16}),
("RiskAversion", "VehicleYear", {"weight": 0.06}),
("SocioEcon", "VehicleYear", {"weight": 0.87}),
("Accident", "ThisCarDam", {"weight": 0.6}),
("RuggedAuto", "ThisCarDam", {"weight": 0.71}),
("MakeModel", "RuggedAuto", {"weight": 0.02}),
("VehicleYear", "RuggedAuto", {"weight": 0.97}),
("Mileage", "Accident", {"weight": 0.83}),
("DrivQuality", "Accident", {"weight": 0.21}),
("Antilock", "Accident", {"weight": 0.18}),
("RiskAversion", "MakeModel", {"weight": 0.18}),
("SocioEcon", "MakeModel", {"weight": 0.3}),
("RiskAversion", "DrivQuality", {"weight": 0.52}),
("DrivingSkill", "DrivQuality", {"weight": 0.43}),
("MakeModel", "Antilock", {"weight": 0.29}),
("VehicleYear", "Antilock", {"weight": 0.61}),
("SeniorTrain", "DrivingSkill", {"weight": 0.14}),
("Age", "DrivingSkill", {"weight": 0.29}),
("RiskAversion", "SeniorTrain", {"weight": 0.37}),
("Age", "SeniorTrain", {"weight": 0.46}),
("Theft", "ThisCarCost", {"weight": 0.79}),
("CarValue", "ThisCarCost", {"weight": 0.2}),
("ThisCarDam", "ThisCarCost", {"weight": 0.51}),
("HomeBase", "Theft", {"weight": 0.59}),
("AntiTheft", "Theft", {"weight": 0.05}),
("CarValue", "Theft", {"weight": 0.61}),
("Mileage", "CarValue", {"weight": 0.17}),
("MakeModel", "CarValue", {"weight": 0.07}),
("VehicleYear", "CarValue", {"weight": 0.95}),
("RiskAversion", "HomeBase", {"weight": 0.97}),
("SocioEcon", "HomeBase", {"weight": 0.81}),
("RiskAversion", "AntiTheft", {"weight": 0.3}),
("SocioEcon", "AntiTheft", {"weight": 0.1}),
("OtherCarCost", "PropCost", {"weight": 0.68}),
("ThisCarCost", "PropCost", {"weight": 0.44}),
("Accident", "OtherCarCost", {"weight": 0.12}),
("RuggedAuto", "OtherCarCost", {"weight": 0.5}),
("Accident", "MedCost", {"weight": 0.03}),
("Cushioning", "MedCost", {"weight": 0.91}),
("Age", "MedCost", {"weight": 0.26}),
]
g = StructureModel(edges)


We will build, in this tutorial, the following plot for this Bayesian Network:

The customisations in the figure above include:

• We order nodes vertically, according to the causality hierarchy

• The edge thickness is proportional to the weight value assigned to the edge

• The figure dimensions obey a standard presentation slide proportions (16:9)

• Color target variables differently from other variables

• Custom node shapes and title

The representation above makes this graph easier to work with than the out-the-box causalnex visualisation (shown below).

[3]:

viz = plot_structure(g)  # Default CausalNex visualisation
image_binary = viz.draw(format="jpg")
Image(image_binary)

[3]:


### Choosing a layout¶

One major change we can make is the layout of the plot. The layout determines how nodes are distributed in the image. In order to Choose a layout, we simply add the argument prog="..." to the draw method.

*Note*: Deciding on the layout is usually the first change we make when customising a visualisation. This is because some of the graph attributes, which we will soon see, only work for certain specific layouts.

The default layout is neato. It finds the node positions by modelling the edges as mechanical springs. The final layout is the equilibrium state.

[4]:

Image(viz.draw(
format="png", prog="circo"  # circo produces a circular layout
),width=500)


[4]:


The layouts available are: dot, neato, fdp, sfdp, twopi and circo. A detailed description of each method can be found on graphviz’s documentation. Graphviz is the visualisation software used by causalnex to create plots).

We show an example of how the different of layouts look like by simulating a tree model.

[5]:

def get_tree(k_list):
"""
Return the edges of a tree given the number of children at each level
"""
n = 1
for level in range(0, len(k_list)):
k = k_list[level]
[(f"A{level}_{i // k}", f"A{level + 1}_{i}") for i in range(k * n)]
)
n = k * n

layouts = [
("dot","Order nodes hierarchly. Great to spot the dependencies of a causal network.",[2, 3, 3]),
("neato", "Spring model. Great default tool if the graph is not too large", [2, 2, 4, 3, 2]),
("sfdp", "A different style of spring model", [2, 2, 4, 3, 2]),
("twopi", "Radial layout", [2, 2, 5, 3]),
]

for layout, description, k_list in layouts:
g_tree = StructureModel(get_tree(k_list))
viz = plot_structure(g_tree)

print(f"{layout}: {description}")
image_binary = viz.draw(format="jpg", prog=layout)
display(Image(image_binary, width=500))


dot: Order nodes hierarchly. Great to spot the dependencies of a causal network.

neato: Spring model. Great default tool if the graph is not too large

sfdp: A different style of spring model

twopi: Radial layout


In this tutorial, we will use the dot layout.

The following is the default result if we use dot. We can see that we have an idea of the dependencies, but the curved edges can be very confusing. We also see overlaps between labels, and this also should be corrected

[6]:

viz = plot_structure(g, prog="dot")
Image(viz.draw(format="jpg"))

[6]:


### How to customise your layout¶

In order to change properties of this plot, we pass graph, nodes and edges attributes. Attributes include the title of the graph, the color or shape of node and the thickness of an edge.

• Graph attributes are passed as a dicionary {attribute : value}.

• Node attributes are of the form {node: {attribute : value}}, i.e., for each node, we pass a dictionary of attributes

• Edge attibutes are of the form {(node_from, node_to): {attribute:value}}.

• The full list of attributes you can set can be found in Graphviz’s documentation on attributes. Since this is an extensive list, we only the main attributes and their meaning in the table below.

A list of useful node, graph and edge attributes:

#### Main Graph Attributes¶

Attribute

Description

values

rankdir

Changes the direction of the hierarchy. By default, nodes are put from top to bottom, according to their rank.

Only works for the dot layout.

• "LR" (Left to Right),

• "TB" (Top to Bottom),

• "RL" or

• "BT"

ranksep

Distance between ranks.

Only works for the dot and twopi layouts.

The suffix "equally" makes this distance to be uniform.

double or string. Examples:

• 1.2

• "1.2 equally"

nodesep

The minimum space between two adjacent nodes in the same rank.

Only works for the dot layout.

double

Ordering

Only works for the dot layout.

By changing the edge order, we can have some control over the position of the nodes in the visualization. See https://www.graphviz.org/doc/info/attrs.html#d:ordering for precise explanation with this attibute.

"in" or "out"

Damping, K

Parameters used by spring models to compute the node positions check https://www.graphviz.org/doc/info/attrs.html#d:Damping for details.

double

splines

Graphviz tries to “curve” the edges to contour nodes, in order to avoid edges overlapping with some nodes. We choose the type of curve it is uses.

A visual example can be found in https://www.graphviz.org/doc/info/attrs.html#d:splines

• "line" - All edges will be STRAIGHT LINES

• "spline" - Use splines

• Others values are: "polynine", "curved", "ortho"

bgcolor

Background graph colour.

“RGB HSV or colour name (black, blue…)”

"transparent" indicates that there is no background color set.

label

A label for the overall graph.

"string"

fontcolor

Colour for the graph label (does not propagates to nodes).

RGB HSV or colour name (black, blue…)

fontname

Font name for the graph label.

"string"

fontsize

Size for the graph label.

double

labelloc

Sets the position of the label vertically.

"t" or "b" (top, bottom)

labeljust

Sets the position of the label horizontally.

"l", "r", "c" (left right center)

dpi

Resolution of image.

double

scale

Scales all graph attributes up or down.

Does not work with dot.

double

pad

Sets a margin in the figure. This margin is exterior to the size of the figure.

string with 2 values, e.g. "1.3,0.8"

size

Sets the dimensions of the figure.

TO MAKE IT WORK AS EXPECTED, add the attribute "ratio=fill" to the graph. This sets the dimensions INSIDE the pad, so the final size is: size + pad value.

string with 2 values, e.g. "16,9"

ratio

If numeric value is provided, it sets the ratio between width and height of the figure. Other options available, in which we pass a string as input.

See the other options here https://www.graphviz.org/doc/info/attrs.html#d:ratio

Numeric value or string ("fill", "compress", "expand", "auto") or not specified

overlap

Resolves overlaps between nodes.

Does not work with dot.

• "true" to retain overlaps

• "false" or prism uses prism algorithm

#### Main Edge Attributes¶

Attribute

Description

values

penwidth

Width of that specific edge.

double

weight

It is a way to indirectly control the edge size. A larger weight encourages the layout to make the edge length Weights in dot must be integers. For dot, larger values makes the edge shorter.

See https://www.graphviz.org/doc/info/attrs.html#d:weight for details

double

label

Edge label, optional.

string

fontcolor, fontsize, fontlabel

Same as for graphs; affects the edge label.

color

Colour of the edge (not its label).

RGB HSV or colour name (black, blue…)

constraint

Works for dot only.

If false, the edge is not used in ranking the nodes. As a result, child and parent may be in the same ranking level. A visual example is in https://www.graphviz.org/doc/info/attrs.html#d:constraint

"true" or "false"

arrowhead

Style of arrowhead. Check https://www.graphviz.org/doc/info/attrs.html#k:arrowType To see all types available

string. E.g.: "open", "vee", "diamond"

arrowsize

Proportion of size of head relative to penwidth

double

#### Main Node Attributes¶

Attribute

Description

Values

pos

Controls the position of a specific node.

For dot: it has NO EFFECT

• "x,y" for setting the node’s initial position to (x,y). This position is modified until the convergence of the algorithm

• "x,y!" to totally fix the position of the node at (x,y)

shape

The shape of the node, a variaty of choices is available.

string

image

Upload an image to be used as a node.

N.B.: Use the attributes imagescale, and imagepos to have more control over the image in the node. See https://www.graphviz.org/doc/info/attrs.html#d:imagepos

Path to the image

style

Information about the node style, whether it is filled, the border is dashed…

One of: solid, dashed, dotted, bold, rounded, diagonals, filled, striped, wedged

fixedsize

If false, the node width and height will be changed so that the label fits inside the node. If true, width and height attributes control this completely.

Check https://www.graphviz.org/doc/info/attrs.html#d:fixedsize for details

"true" or "false"

width

Width of node.

If fixedsize is false, this is the minimal width.

double

height

Height of node. If fixed size is false, this is the minimal height.

double

regular

If regular is true, width and height are set to the same value.

"true" or "false"

penwidth

Specifies the width of the pen, in points, used to the boundaries of node.

double

color

Colour the node boundary. Check https://graphviz.gitlab.io/_pages/doc/info/colors.html to see all options

RGB, HSV or colour name (black, blue, red…)

fillcolor

Colour inside the node.

RGB, HSV or colour name (black, blue, red…)

label

Label for the node. If not specified, the node name is used as label.

N.B.: We can write rich text by writing the node in HTML. The guide to do so is here https://www.graphviz.org/doc/info/shapes.html#html

string

labelloc

Label position inside the node: bottom, top or centre.

b, t or c

fontcolor, fontsize, fontlabel

Same as for graphs; affects the node label.

#### Example of changing parameters¶

As an example of how much of the visualisation can be customised, we use almost almost all the attributes from the table above to modify the visualisation. The result is purposely not pleasing, but shows how to obtain a very high level of control over the image.

[7]:

graph_attributes = {
"rankdir": "LR",  # Change ranking direction to be horizontal
"splines": "false",  # Do not curve edges, use straight lines instead
"bgcolor": "orange",  # background color
"label": "An ugly plot\nto exemplify how many customisations are possible",
"fontcolor": "red",  # Setting label font
"fontname": "Times",  # Setting label font settings
"fontsize": 20,  # Setting LABEL font settings
"pad": "0.8,0.3",  # setting a margin
"dpi": 120,  # resolution
"labeljust": "l",  # This sets the title to be at the left
"labelloc": "t",  # This sets the title to be at the top
"nodesep": 0.2,  # separation between nodes with same rank
"ranksep": 1.1,  # This changes the distances between rank levels in hierarchy (For Dot and twopi only )
}

# Changing attributes of specific nodes
node_attributes = {
"Age": {  # We change the attributes of the node "Age"
"shape": "square",
"style": "dashed",
"width": 1,
"penwidth": "4",  # Thickness of the boundary
"color": "#4a90e2d9",
"orientation": 25,  # rotate node
},
"Mileage": {
"shape": "hexagon",
"regular": "true",  # forces the polygon to be regular
"color": "green",
},
"Cushioning": {
"shape": "star",
"label": "This is a star",  # Label overwrites the default nae
},
"SeniorTrain": {
"image": "./supporting_files/cat.jpeg",  # we can upload local images inside a node
"width": 1.2,
"shape": "dot",  # choose node to be a dot, so that the image is larger than the node
},
}

# Changing attributes of specific edges
edge_attributes = {
("SocioEcon", "OtherCar"): {
"label": "this is an edge label",  # Edges can have labels
"fontcolor": "chocolate",  # setting the label color
},
("SocioEcon", "GoodStudent"): {"color": "blue"},
("SocioEcon", "RiskAversion"): {
"constraint": "false"
},  # edge not used for ranking, both extremities are on same level
("SocioEcon", "VehicleYear"): {"penwidth": 15},  # Thickness of edge
}

viz = plot_structure(
g,
prog="dot",
graph_attributes=graph_attributes,
node_attributes=node_attributes,
edge_attributes=edge_attributes,
)
display(Image(viz.draw(format="jpg")))


#### Optimising the network design¶

The next step is to use all this customisation power to actually make the visualisation more appealing and meaningful. The result could easily be used in applications such as presentations or papers, with only minor post processing, if any.

Among the customisations made in the plot below, we emphasise the following:

• Color target variables differently from other nodes

• Use edge weights (or any meaningful quantitative value related to an edge) to set the thickness of an edge.

• Choose wisely the layout (in this case dot) that suits your application, and the parameters to allocate the nodes

[8]:

graph_attributes = {
"splines": "spline",  # I use splies so that we have no overlap
"ordering": "out",
"ratio": "fill",  # This is necessary to control the size of the image
"size": "16,9!",  # Set the size of the final image. (this is a typical presentation size)
"label": "The structure of our\n \t Insurance model",
"fontcolor": "#FFFFFFD9",
"fontname": "Helvetica",
"fontsize": 100,
"labeljust": "l",
"labelloc": "t",
"dpi": 200,
"nodesep": 0.8,
"ranksep": ".5 equally",
}

# Making all nodes hexagonal with black coloring
node_attributes = {
node: {
"shape": "hexagon",
"width": 2.2,
"height": 2,
"fillcolor": "#000000",
"penwidth": "10",
"color": "#4a90e2d9",
"fontsize": 35,
"labelloc": "c",
}
for node in g.nodes
}

# Splitting two words with "\n"
for node in g.nodes:
up_idx = [i for i, c in enumerate(node) if c.isupper()][-1]
node_attributes[node]["label"] = node[:up_idx] + "\n" + node[up_idx:]

# Target nodes (ones with "Cost" in the name) are colored differently
for node in g.nodes:
if "Cost" in node:  # We color nodes with "cost" in the name with a orange colour.
node_attributes[node]["fillcolor"] = "#DF5F00"

# Customising edges
edge_attributes = {
(u, v): {
"penwidth": w * 20 + 2,  # Setting edge thickness
"weight": int(5 * w),  # Higher "weight"s mean shorter edges
"arrowsize": 2 - 2.0 * w,  # Avoid too large arrows
"arrowtail": "dot",
}
for u, v, w in g.edges(data="weight")
}

viz = plot_structure(
g,
prog="dot",
graph_attributes=graph_attributes,
node_attributes=node_attributes,
edge_attributes=edge_attributes,
)
f = "supporting_files/final_insurance_model.jpg"
viz.draw(f)
Image(f)

[8]:


If fixing the image size is not a requirement, we obtain the following image.

[9]:

# Remove attributes fixing the size of figure
del graph_attributes["size"]
del graph_attributes["ratio"]

# minor changes on distancing
graph_attributes["nodesep"] = 2
graph_attributes["ranksep"] = "1.1 equally"
graph_attributes["label"] = "This is the structure if size is\nnot fixed"

viz = plot_structure(
g,
prog="dot",
graph_attributes=graph_attributes,
node_attributes=node_attributes,
edge_attributes=edge_attributes,
)
display(Image(viz.draw(format="jpg")))


### Subgraphs and Clusters (Advanced topic)¶

Subgraphs and Clusters are a feature of Graphviz. Their role is as follows:

• A subgraph is created by specifying a set of nodes. The subgraph provides a context for setting attributes: we can set graph, node, edge attributes that are only valuable for this subgraph.

• A cluster is a subgraph whose name has the prefix cluster. This prefix tells the layout engine (i.e. dot, neato, fdp,…) to draw the nodes in the subgraph together. The result is that the nodes are “clustered” together and there will be a bounding box around them.

In order to create a subgraph or cluster, we need run the method subgraph of the object returned by plot_structure.

Note: We have to run viz.layout(prog = <chosen_layout>) after creating a cluster. This is because positions may become non deterministic once we create clusters.

Below, we show a few examples of this functionality:

[10]:

g_test = StructureModel(
[
("g", "d"),
("h", "e"),
("g", "h"),
("e", "d"),
("c", "f"),
("h", "f"),
("b", "e"),
("a", "f"),
("i", "a"),
("d", "i"),
("c", "e"),
("c", "g"),
("e", "i"),
("g", "b"),
("d", "i"),
("b", "i"),
("j", "k"),
("l", "m"),
("n", "m"),
("n", "m"),
("o", "p"),
("o", "q"),
("q", "l"),
]
)

viz = plot_structure(
g_test,
prog="dot",
graph_attributes={"dpi": 200, "nodesep": 1, "ranksep": ".5 equally"},
)

print("Graph with with no clusters")
display(Image(viz.draw(format="jpg")))

print("Graph with clusters and subgraphs added")
# This Subgraph sets the nodes 'o','p','q' to have the same rank, i.e. be on the same level
subgraph = viz.subgraph(["o", "p", "q"], name="same_level_subraph")
subgraph.graph_attr.update({"rank": "same"})
# This is a cluster, since the name starts with "cluster". Note the white retangular box around it
subgraph = viz.subgraph(["j", "k"], name="cluster_1", label="Some cluster")
subgraph.graph_attr.update({"color": "white"})
# A cluster with background color different from the rest of the graph
subgraph = viz.subgraph(["g", "b", "i", "a"], name="cluster2", label="Blue cluster")
subgraph.graph_attr.update({"color": "white", "bgcolor": "cornflowerblue"})
# Another cluster, this time transparent
subgraph = viz.subgraph(["l", "m", "n"], name="cluster3", label="Transparent Cluster")
subgraph.graph_attr.update({"color": "transparent"})

## It is important to run this before draw to get the desired effect
viz.layout("dot")
display(Image(viz.draw(format="jpg")))


Graph with with no clusters

Graph with clusters and subgraphs added


## Understand the engine used in CausalNex visualisations¶

The plots we have seen are all rendered by Graphviz. The interface between causalnex networks and Graphviz is done by a Python package named pygraphviz.

### Understaning Graphviz¶

Graphviz renders networks represented in a language called dot. An example of a simple network in dot format is shown bellow:

digraph G {
graph [dpi=100];
a [color=blue, shape=cylinder]
a -> b[color=red];
a -> c;
}


Once you have Graphviz installed, if we run the following command on the command line:

dot -Tjpg simple_graph.dot > output.jpg


The dot engine will render the graph below. We will obtain the following:

We could also run for example:

neato -Tjpg simple_graph.dot > output.jpg


In which case we would obtain a neato style layout.

### How does this relate to CausalNex?¶

When we run plot_structure, the network structure and attributes on the dictionaries (graph_ edge_ and node_attributes) are translated to dot language. This translation is done by pygraphviz.

### The role of pygraphviz¶

plot_structure returns a pygraphviz object (an AGraph) which internally stores a structure in dot format. If we’d like to see this structure, we can run viz.string()

[11]:

viz = plot_structure(g)
print(viz.string()[:470])

strict digraph "" {
graph [bb="0,0,687.24,701.89",
bgcolor="#001521",
dpi=80,
fontcolor="#FFFFFFD9",
fontname=Helvetica,
overlap=scale,
scale=2.0,
splines=True
];
node [label="\N"];
Age     [color="#4a90e220",
fillcolor="#4a90e2d9",
fixedsize=True,
fontcolor="#FFFFFFD9",
fontname=Helvetica,
fontsize=15,
height=0.15278,
label="Age

",
penwidth=20,
pos="405.58,175.74",
shape=circle,
style=filled,
width=0.15278];



This can be useful for verification purposes and to see default values of attributes.

## Alternative solutions¶

### Plotting with networkx¶

Since a CausalNex’s StructureModel is an extension of networkx graphs, we can easily use networkx to plot our structures.

[12]:

import networkx as nx
import matplotlib.pyplot as plt
import matplotlib as mpl

mpl.rcParams["figure.dpi"] = 120

fig = plt.figure(figsize=(15, 8))  # set figsize
nx.draw_networkx(g)


Advantages of using networkx:

• Plotting with networkx can be much simpler since it uses matplotlib to create the graph. Anyone familiar with matplotlib can use it to customise the graph to his/her needs.

• We have much more control over the image since we have all matplotlib functionality available. We can, for example, easily change the positions of a node by hand.

• Documentation is more readable, since it is purely in Python.

• Features like splines on edges, gradient colored edges are not readily available in networkx.

• Layouts in Graphviz tend to produce better node positions. While networkx supports calling Graphviz to obtain positions, it can be inconvenient to pass all layout parameters (like rankdir K or Damping) through the API provided.

• networkx images may need fine tuning in the end.

We exemplify below how to obtain, with networkx, similar plots to what we got with plot_structure.

[13]:

fig = plt.figure(figsize=(15, 8))  # set figsize
ax.set_facecolor("#001521")  # set backgrount

### run a layout algorithm to set the position of nodes
# pos = nx.drawing.layout.circular_layout(g) # various layouts available
# pos = nx.drawing.layout.planar_layout(g)
# pos = nx.drawing.layout.random_layout(g)
# pos = nx.drawing.layout.rescale_layout(g)
# pos = nx.drawing.layout.shell_layout(g)
# pos = nx.drawing.layout.spring_layout(g)
# pos = nx.drawing.layout.spectral_layout(g)
# pos = nx.drawing.layout.spiral_layout(g)
# pos = nx.drawing.nx_agraph.graphviz_layout(g, prog="neato")
pos = nx.drawing.nx_agraph.graphviz_layout(g, prog="dot")

# We can change the position of specific nodes
pos["Cushioning"] = (705.82, 200.0)
pos["SeniorTrain"] = (500.82, 600.0)

nx.draw_networkx_nodes(
g,
pos,
node_shape="H",
node_size=1000,
linewidths=3,
edgecolors="#4a90e2d9",
node_color=["black" if "Cost" not in el else "#DF5F00" for el in g.nodes],
)
nx.draw_networkx_labels(
g,
pos,
font_color="#FFFFFFD9",
font_weight="bold",
font_family="Helvetica",
font_size=10,
)
nx.draw_networkx_edges(
g,
pos,
edge_color="white",
node_shape="H",
node_size=2000,
node_color="black",
width=[w + 0.1 for _, _, w, in g.edges(data="weight")],
)

plt.text(660, 650, "The structure of our\n Insurance model", color="white", size=20)


[13]:

Text(660, 650, 'The structure of our\n Insurance model')


## References¶

[1] J. Binder, D. Koller, S. Russell, and K. Kanazawa. Adaptive Probabilistic Networks with Hidden Variables. Machine Learning, 29(2-3):213-244, 1997.)

Note

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