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<py-env>

- numpy

- networkx

- matplotlib

</py-env>

<py-script>

import numpy as np

import networkx as nx

</py-script>

<p>Message passing with linear algebra: a demo.</p>

<p>Imagine we have a chain graph that looks like this:</p>

<pre><code>O --> 1 --> 2 --> 3</code></pre>

<p>In NetworkX this graph would look like the following:</p>

<pre>

<py-script>

G = nx.Graph()

nodes = list(range(4))

G.add_edges_from(zip(nodes[0:-1], nodes[1:]))

print(G.edges())

<p>This chain graph has the following adjacency matrix:</p>

<pre>

adj_mat = np.eye(4, k=1)

print(f"A: {adj_mat}")

</pre>

<p>And imagine that we have a message that lives on the graph:</p>

<pre>

<py-script>

message = np.array([1.0, 0.0, 0.0, 0.0])

print(f"message: {message}")

</py-script>

</pre>

<p>Try out message passing below by doing any one of the following steps:</p>

<pre><code>message @ adj_mat</code></pre>

<pre><code>message @ adj_mat @ adj_mat</code></pre>

<pre><code>message @ adj_mat @ adj_mat @ adj_mat</code></pre>

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