IEEE Computational Intelligence Magazine - February 2021 - 103

the StellarGraph library for GNNs
which, like Spektral, is based on Keras.
This library implements six messagepassing layers, four of which are available in Spektral (GCN, GraphSAGE,
GAT and APPNP), but does not offer
pooling layers and relies on a custom
format for graph data, which limits
flexibility. Finally, the graph_nets
package9 implements Graph Networks
as proposed by Battaglia et al. [1]. However, the package is not a full library for
GNNs and only offers a general interface that users can extend.
Spektral is currently the most feature-rich library for GNNs in TensorFlow. The extensive collection of
examples and tutorials, the Keras integration, and the transparent handling
of different data modes make it
extremely easy for new users to familiar ize with GNNs, while its good
computational performance and variety of available methods make Spektral a sensible choice even for
advanced use cases.

mental settings described in the original
papers, but we use the random data
splits suggested by Shchur et al. [51] for
a fairer evaluation.

To evaluate the pooling layers, DiffPool
[29], MinCut [31], Top-K [30], and
SAGPool [41], we consider a task of
graph-level classification, where each
graph represents an individual sample
to be classified. We use four datasets
from the Benchmark Data Sets for
Graph Kernels: Proteins, IMDB-Binary,
Mutag and NCI1. Here, we adopt a
fixed GNN architecture (described in
Appendix A) where we only change
the pooling method. To assess whether
each pooling layer is actually beneficial
for learning a representation of the data,
we also evaluate the same GNN without pooling (Flat).

quantum molecular properties using
the QM9 database of small molecules.
We train a GNN on four different continuous targets for graph-level regression: dipole moment (Mu), isotropic
polar izability (Alpha), energy of
HOMO (Homo), and internal energy
at OK (U0).
Since the molecules in QM9 have
attributed edges, we adopt a GNN
based on ECC, which is designed to
integrate edge attributes in the messagepassing operation. We note that the
architecture used for this experiment is
significantly smaller and simpler than the
current state of the art [52], and that
these results are only meant to show a
comparison between the different global
pooling methods, rather than replicating
the exact performance figures of other
works (which may be significantly different than what we report).

C. Graph Regression

D. Results

To evaluate the global pooling methods, we consider the task of predicting

The results for each experiment are
reported in Tables II, III, and IV. In the

B. Graph Classification

IV. Applications

In this section, we report some experimental results on several well-known
benchmark tasks, in order to provide a
high-level overview of how the different
methods implemented by Spektral perform in a standard research use case scenario. We report the results for three
main settings: a node classification task
and two tasks of graph-level property
prediction, one of classification and one
of regression. All experimental details are
reported in Appendix A.
A. Node Classification

In our first experiment, we consider a
task of semi-supervised node classification on the Cora, CiteSeer, and Pubmed
citation networks. In these datasets,
nodes represent text documents and the
undirected edges represent citations. The
task consists of classifying the documents
into a finite number of subject areas. We
evaluate GCN [22], ChebNet [21],
ARMA [26], GAT [24] and APPNP
[28]. We reproduce the same experi9

https://github.com/deepmind/graph_nets

TABLE I Comparison of different GNN libraries. The Framework column indicates
the backend framework supported by the library, while the MP and Pooling
columns indicate the number of different message-passing and pooling layers
implemented by the library, respectively.
LIBRARY

FRAMEWORK

POOLING

Spektral

TensorFlow

PyG

PyTorch

DGL

PyTorch, others

graph_nets

TensorFlow

N/A

StellarGraph

TensorFlow

N/A

TABLE II Classification accuracy on the node classification tasks.
Dataset

ChebNet

GCN

GAT

ARMA

APPNP

CORA

77.4 ± 1.5

79.4 ± 1.3

82.0 ± 1.2

80.5 ± 1.2

82.8 ± 0.9

CITESEER

68.2 ± 1.6

68.8 ± 1.4

70.0 ± 1.0

70.6 ± 0.9

70.0 ± 1.0

PUBMED

74.0 ± 2.7

76.6 ± 2.5

73.8 ± 3.3

77.2 ± 1.6

78.2 ± 2.1

TABLE III Classification accuracy on the graph classification tasks.
Dataset

Flat

MinCut

DiffPool

Top-K

SAGPool

Proteins

74.3 ± 4.5

75.5 ± 2.0

74.1 ± 3.9

70.5 ± 3.4

71.3 ± 5.0

IMDB-B

72.8 ± 7.2

73.6 ± 5.4

70.6 ± 6.6

67.7 ± 8.2

69.3 ± 5.7

Mutag

72.5 ± 14.0

81.4 ± 10.7

83.5 ± 9.7

79.2 ± 8.0

78.5 ± 8.3

NCI1

77.3 ± 2.6

74.4 ± 1.9

71.1 ± 3.0

72.0 ± 3.0

69.4 ± 8.4

FEBRUARY 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

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https://github.com/deepmind/graph_nets

IEEE Computational Intelligence Magazine - February 2021

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