## Getting started

Spektral is designed according to the guiding principles of Keras to make things extremely simple for beginners while maintaining flexibility for experts.

In this page we will go over the main features of Spektral while creating a graph neural network for graph classification.

### Graphs

A graph is a mathematical object that represents relations between objects. We call the objects "nodes" and the relations "edges".

Both the nodes and the edges can have vector features.

In Spektral, graphs are represented with instances of spektral.data.Graph which can contain:

• a: the adjacency matrix - usually a scipy.sparse matrix of shape (n_nodes, n_nodes).
• x: the node features - represented by a np.array of shape (n_nodes, n_node_features).
• e: the edge features - usually represented in a sparse edge list format, with a np.array of shape (n_edges, n_edge_features).
• y: the labels - can represent anything, from graph labels to node labels, or even something else.

A graph can have all of these attributes or none of them. Since Graphs are just plain Python objects, you can also add extra attributes if you want. For instance, see graph.n_nodes, graph.n_node_features, etc.

### Datasets

The spektral.data.Dataset container provides some useful functionality to manipulate collections of graphs.

Let's load a popular benchmark dataset for graph classification:

>>> from spektral.datasets import TUDataset

>>> dataset = TUDataset('PROTEINS')

>>> dataset
TUDataset(n_graphs=1113)


We can now retrieve individual graphs:

>>> dataset[0]
Graph(n_nodes=42, n_node_features=4, n_edge_features=None, y=[1. 0.])


or shuffle the data:

>>> np.random.shuffle(dataset)


or slice the dataset up into sub-datsets:

>>> dataset[:100]
TUDataset(n_graphs=100)


Datasets also provide methods for applying transforms to each data:

• apply(transform) - modifies the dataset in-place, by applying the transform to each graph;
• map(transform) - returns a list obtained by applying the transform to each graph;
• filter(function) - removes from the dataset any graph for which function(graph) is False. This is also an in-place operation.

For example, let's modify our dataset so that we only have graphs with less than 500 nodes:

>>> dataset.filter(lambda g: g.n_nodes < 500)

>>> dataset
TUDataset(n_graphs=1111)  # removed 2 graphs


Now let's apply some transforms to our graphs. For example, we can modify each graph so that the node features also contain the one-hot-encoded degree of the nodes.

First, we compute the maximum degree of the dataset, so that we know the size of the one-hot vectors:

>>> max_degree = dataset.map(lambda g: g.a.sum(-1).max(), reduce=max)

>>> max_degree
12


Try to go over the lambda function to see what it does. Also, notice that we passed another function to the method with the reduce keyword. Can you guess why?

Now we are ready to augment our node features with the one-hot-encoded degree. Spektral has a lot of pre-implemented transforms that we can use:

>>> from spektral.transforms import Degree

>>> dataset.apply(Degree(max_degree))


We can see that it worked because now we have an extra max_degree + 1 node features:

>>> dataset[0]
Graph(n_nodes=42, n_node_features=17, n_edge_features=None, y=[1. 0.])


Since we will be using a GCNConv layer in our GNN, we also want to follow the original paper that introduced this layer and do some extra pre-processing of the adjacency matrix.

Since this is a fairly common operation, Spektral has a transform to do it:

>>> from spektral.transforms import GCNFilter

>>> dataset.apply(GCNFilter())


Many layers will require you to do some form of preprocessing. If you don't want to go back to the literature every time, every convolutional layer in Spektral has a preprocess(a) method that you can use to transform the adjacency matrix as needed.
Have a look at the handy LayerPreprocess transform.

### Creating a GNN

Creating GNNs is where Spektral really shines. Since Spektral is designed as an extension of Keras, you can plug any Spektral layer into a Keras Model without modifications.
We just need to use the functional API because GNN layers usually need two or more inputs (so no Sequential models for now).

For our first GNN, we will create a simple network that first does a bit of graph convolution, then sums all the nodes together (known as "global pooling"), and finally classifies the result with a dense softmax layer.
Oh, and we will also use dropout for regularization.

Let's start by importing the necessary layers:

from tensorflow.keras.models import Model
from tensorflow.keras.layers import Dense, Dropout
from spektral.layers import GCNConv, GlobalSumPool


Now we can use model subclassing to define our model:

class MyFirstGNN(Model):

def __init__(self, n_hidden, n_labels):
super().__init__()
self.graph_conv = GCNConv(n_hidden)
self.pool = GlobalSumPool()
self.dropout = Dropout(0.5)
self.dense = Dense(n_labels, 'softmax')

def call(self, inputs):
out = self.graph_conv(inputs)
out = self.dropout(out)
out = self.pool(out)
out = self.dense(out)

return out


And that's it.

Note how we mixed layers from Spektral and Keras interchangeably: it's all just computation with tensors underneath!

This also means that if you want to break free from Graph and Dataset and every other feature of Spektral, you can.

Note: If you don't want to subclass Model to implement your GNN, you can also use the classical declarative style. You just need to pay attention to the Input and leave "node" dimensions unspecified (so None instead of n_nodes).

### Training the GNN

Now we're ready to train the GNN. First, we instantiate and compile our model:

model = MyFirstGNN(32, dataset.n_labels)


and we're almost there!

However, here's where graphs get in our way. Unlike regular data, like images or sequences, graphs cannot be stretched or cut or reshaped so that we can fit them into tensors of pre-defined shape. If a graph has 10 nodes and another one has 4, we have to keep them that way.

This means that iterating over a dataset in mini-batches is not trivial and we cannot simply use the model.fit() method of Keras as-is.

We have to use a data Loader.

Loaders iterate over a graph dataset to create mini-batches. They hide a lot of the complexity behind the process, so that you don't need to think about it. You only need to go to this page and read up on data modes, so that you know which loader to use.

Each loader has a load() method that when called will return a data generator that Keras can process.

Since we're doing graph-level classification, we can use a BatchLoader. It's a bit slow and memory intensive (a DisjointLoader would have been better), but it lets us simplify the definition of MyFirstGNN. Again, go read about data modes after this tutorial.

from spektral.data import BatchLoader



and we can finally train our GNN!

Since loaders are essentially generators, we need to provide the steps_per_epoch keyword to model.fit() and we don't need to specify a batch size:

model.fit(loader.load(), steps_per_epoch=loader.steps_per_epoch, epochs=10)


Done!

### Evaluating the GNN

Evaluating the performance of our model, be it for testing or validation, follows a similar workflow.

from spektral.data import BatchLoader



and feed it to the model by calling load():

loss = model.evaluate(loader.load(), steps=loader.steps_per_epoch)

print('Test loss: {}'.format(loss))


### Node-level learning

Besides learning to predict labels for the whole graph, like in this tutorial, GNNs are very effective at learning to predict labels for each node. This is called "node-level learning" and we usually do it for datasets with one big graph (think a social network).

For example, reproducing the results of the GCN paper for classifying nodes in a citation network can be done with GCNConv layers, the Citation dataset, and a SingleLoader: check out this example.

As a matter of fact, check out all the examples.

### Go create!

You are now ready to use Spektral to create your own GNNs.

If you want to build a GNN for a specific task, chances are that everything you need is already in Spektral. Check out the examples for some ideas and practical tips.

Remember to read the data modes section to learn about representing graphs and creating mini-batches.

Make sure to read the documentation, and get in touch on Github if you have a feature that you want to see implemented.

If you want to cite Spektral in your work, refer to our paper:

Graph Neural Networks in TensorFlow and Keras with Spektral
Daniele Grattarola and Cesare Alippi