# Basic UsageΒΆ

Let’s make a simple 3-node network and compute its \(\Phi\).

To make a network, we need a TPM and (optionally) a connectivity matrix. The
TPM can be in more than one form; see the documentation for
`pyphi.network`

. Here we’ll use the 2-dimensional state-by-node form.

```
>>> import pyphi
>>> import numpy as np
>>> tpm = np.array([
... [0, 0, 0],
... [0, 0, 1],
... [1, 0, 1],
... [1, 0, 0],
... [1, 1, 0],
... [1, 1, 1],
... [1, 1, 1],
... [1, 1, 0]
... ])
```

The connectivity matrix is a square matrix such that the \(i,j^{\textrm{th}}\) entry is 1 if there is a connection from node \(i\) to node \(j\), and 0 otherwise.

```
>>> cm = np.array([
... [0, 0, 1],
... [1, 0, 1],
... [1, 1, 0]
... ])
```

Now we construct the network itself with the arguments we just created:

```
>>> network = pyphi.Network(tpm, connectivity_matrix=cm)
```

The next step is to define a subsystem for which we want to evaluate \(\Phi\). To make a subsystem, we need the network that it belongs to, the state of that network, and the indices of the subset of nodes which should be included.

The state should be an \(n\)-tuple, where \(n\) is the number of nodes in the network, and where the \(i^{\textrm{th}}\) element is the state of the \(i^{\textrm{th}}\) node in the network.

```
>>> state = (1, 0, 0)
```

In this case, we want the \(\Phi\) of the entire network, so we simply include every node in the network in our subsystem:

```
>>> subsystem = pyphi.Subsystem(network, state, range(network.size))
```

Now we use `pyphi.compute.big_phi()`

function to compute the \(\Phi\) of
our subsystem:

```
>>> phi = pyphi.compute.big_phi(subsystem)
>>> phi
2.3125
```

If we want to take a deeper look at the integrated-information-theoretic
properties of our network, we can access all the intermediate quantities and
structures that are calculated in the course of arriving at a final \(\Phi\)
value by using `pyphi.compute.big_mip()`

. This returns a deeply nested
object, `BigMip`

, that contains data about the subsystem’s constellation of
concepts, cause and effect repertoires, etc.

```
>>> mip = pyphi.compute.big_mip(subsystem)
```

For instance, we can see that this network has 4 concepts:

```
>>> len(mip.unpartitioned_constellation)
4
```

The documentation for `pyphi.models`

contains description of these
structures.

Note

Networks can be constructed with an optional set of textual labels for each node:

```
>>> labels = ('A', 'B', 'C')
>>> network = pyphi.Network(tpm, cm, node_labels=labels)
```

These labels must be unique. We can then use these labels when constructing
a `Subsystem`

:

```
>>> pyphi.Subsystem(network, state, ('B', 'C'))
Subsystem((B, C))
```

Note

The network and subsystem discussed here are returned by the
`pyphi.examples.basic_network()`

and
`pyphi.examples.basic_subsystem()`

functions.