

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
The GNN simulator, along with the benchamarks used in [1,2], and a short manual is available for
download in the following page.
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
relational learning: an experimental comparison. Machine
Learning, 82(3):315349, 2011.
 D. Muratore, M. Hagenbuchner, F. Scarselli, and A. Tsoi.
Sentence extraction by graph neural networks. Artificial
Neural Networksâ€“ICANN 2010, pages 237246, 2010.
 S. Zhang, M. Hagenbuchner, F. Scarselli, and A. Tsoi.
Supervised encoding of graphofgraphs for classification
and regression problems. Focused Retrieval and Evaluation,
pages 449461, 2010.
 V. Di Massa, G. Monfardini, L. Sarti, F. Scarselli, M. Maggini,
and M. Gori. A comparison between recursive neural
networks and graph neural networks. In International
Joint Conference on Neural Networks, pages 778785,
July 2006.
 Gabriele Monfardini, Vincenzo Di Massa, Franco
Scarselli, and Marco Gori. Graph neural networks for
object localization. In Proceedings of the 2006 conference
on ECAI 2006: 17th European Conference on Artificial Intelligence
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 F. Scarselli, S.L. Yong, M. Gori, M. Hagenbuchner, A.C.
Tsoi, and M. Maggini. Graph Neural Networks for ranking
web pages. In Proceedings of the 2005 IEEE/WIC/ACM
Conference on Web Intelligence, WI2005, pages 666672,
Washington, DC, USA, 2005. IEEE Computer Society.
 S.L. Yong, M. Hagenbuchner, F. Scarselli, A. C. Tsoi, and
M. Gori. Document mining using Graph Neural Networks.
In Norbert Fuhr, Mounia Lalmas, and Andrew Trotman,
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of the Initiative for the Evaluation of XML Retrieval,
INEX 2006, Revised and Selected Papers, volume 4518
of Lecture Notes in Computer Science, pages 458472.
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