

The Graph Neural Network model
The Graph Neural Network (GNN) is a novel connectionist
model particularly suited for problems
whose domain can be represented by a set of patterns and relationships
between them [1,2]. In those problems, a prediction about a given
pattern can
be
carried out exploiting all the related information, which includes the
pattern features, the pattern relationships
and, in general, the whole graph that represents the domain. GNN
peculiarity consists in its
capability of making the prediction taking directly in input the domain
graph, without any preprocessing. In this sense, the GNN methods is
different from the common approach, which face a domain with
relationship by an ad hoc preprocessing procedure that compresses into
a vectorial representation all the data about a pattern. Actually, GNNs
can be considered the connectionist counterpart of SVM for graphs and
random fields.
GNNs have been proved to
be sort of universal approximator for functions on graphs and have been
applied to several problems, including spam detection, object
localization in images, molecule classification.
The GNN software
A new version of the GNN package is now available for Tensorflow (by Alberto Rossi and Matteo Tiezzi).
References
Definition and properties of the GNN model
 F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, G.
Monfardini.The Graph Neural Network
Model. IEEE
Transactions on Neural Networks, vol. 20(1); p. 6180, 2009.
 F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, G.
Monfardini. Computational Capabilities
of Graph Neural Networks. IEEE
Transactions on Neural Networks, vol. 20(1); p. 81102, 2009.
Applications of GNNs
 L. Di Noi, M. Hagenbuchner, F. Scarselli, and A. Tsoi.
Solving graph data issues using a layered architecture
approach with applications to web spam detection. Neural Networks, 48, pages 7890, 2013.

N. Bandinelli, B. Bianchini, and F. Scarselli.
Learning longterm dependencies using layered graph neural networks.
In The 2012 International Joint Conference on Neural Networks, pages 18, 2012.
 W. Uwents, G. Monfardini, H. Blockeel,
M. Gori, and F. Scarselli. Neural networks for
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Learning, 82(3):315349, 2011.
 D. Muratore, M. Hagenbuchner, F. Scarselli, and A. Tsoi.
Sentence extraction by graph neural networks. Artificial
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 S. Zhang, M. Hagenbuchner, F. Scarselli, and A. Tsoi.
Supervised encoding of graphofgraphs for classification
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 V. Di Massa, G. Monfardini, L. Sarti, F. Scarselli, M. Maggini,
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 Gabriele Monfardini, Vincenzo Di Massa, Franco
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 F. Scarselli, S.L. Yong, M. Gori, M. Hagenbuchner, A.C.
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 S.L. Yong, M. Hagenbuchner, F. Scarselli, A. C. Tsoi, and
M. Gori. Document mining using Graph Neural Networks.
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