Computational Capabilities of Graph Neural Networks

Scarselli, Franco; Gori, Marco; Tsoi, Ah Chung; Hagenbuchner, Markus; Monfardini, Gabriele

doi:10.1109/tnn.2008.2005141

Cited by 194 publications

(119 citation statements)

References 29 publications

Supporting

Mentioning

116

Contrasting

Order By: Relevance

“…e now restate the definition of an unfolding tree-first given by Scarselli et al [3]-which leads to a natural equivalence relation between vertices of a given graph. Informally, the unfolding tree of a vertex v in a labelled graph G can be thought of as a decision tree of walks starting at v in G. We start with a vertex corresponding to the length 0 walk ⟨v⟩, and then connect all of the length 1 walks starting at v to the vertex ⟨v⟩.…”

Section: Chaptermentioning

confidence: 99%

“…nfolding trees were first presented by Scarselli et al in a paper on their Graph Neural Network (GNN) model [3]. The GNN model is a neural net architecture designed to predictively model properties of graph-structured data, such as molecular structures or a set of interlinked web pages.…”

mentioning

confidence: 99%

“…INTRODUCTION rectly reduced to an extant graph-theoretic concept-unfolding trees are inherently intriguing. In addition to this, the original formulation in [3] lacked the rigor proper to mathematics. And, of course, the dearth of previous research promised fertile mathematical ground.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Unfolding Trees and Symmetrically-Associated Graphs

Flowerday

2015

View full text Add to dashboard Cite

An unfolding tree is an object reflecting the connectivity properties of a vectorlabelled graph. First introduced in the context of theoretical computer science as a way of describing information flow in a neural net model of graph-structured data, unfolding trees have remained unexplored within graph theory. They give rise to an equivalence relation on the vertices of a graph, one which describes the connective environments of vertices but is not reducible to automorphism group orbits. This thesis formalizes unfolding trees and investigates their properties along with the implications of this vertex relation. This leads to the graph property of symmetric-association; graphs with this property have predictably-behaved unfolding trees. Symmetric-association is presented as a generalization of k-regularity, culminating in a Havel-Hakimi type result featuring a graph transformation that preserves unfolding trees.i

show abstract

Section: Chaptermentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Unfolding Trees and Symmetrically-Associated Graphs

Flowerday

2015

View full text Add to dashboard Cite

show abstract

“…Examples include structured data such as bioinformatics sequences, graphs, or tree structures as they occur in linguistics, time series data, functional data arising in mass spectrometry, relational data stored in relational databases, etc. In consequence, a variety of techniques has been developed to extend powerful statistical machine learning tools towards non-vectorial data such as kernel methods using structure kernels, recursive and graph networks, functional methods, relational approaches, and similar [9,12,5,27,6,26,10,11]. One very prominent way to extend statistical machine learning tools is offered by the choice of problemspecific measures of data proximity, which can often directly be used in machine learning tools based on similarities, dissimilarities, distances, or kernels.…”

Section: Introductionmentioning

confidence: 99%

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

Mokbel

Groß

Lux

et al. 2012

Artificial Neural Networks in Pattern Recognition

View full text Add to dashboard Cite

For complex data sets, the pairwise similarity or dissimilarity of data often serves as the interface of the application scenario to the machine learning tool. Hence, the final result of training is severely influenced by the choice of the dissimilarity measure. While dissimilarity measures for supervised settings can eventually be compared by the classification error, the situation is less clear in unsupervised domains where a clear objective is lacking. The question occurs, how to compare dissimilarity measures and their influence on the final result in such cases. In this contribution, we propose to use a recent quantitative measure introduced in the context of unsupervised dimensionality reduction, to compare whether and on which scale dissimilarities coincide for an unsupervised learning task. Essentially, the measure evaluates in how far neighborhood relations are preserved if evaluated based on rankings, this way achieving a robustness of the measure against scaling of data. Apart from a global comparison, local versions allow to highlight regions of the data where two dissimilarity measures induce the same results.

show abstract

“…GNNs have been proposed to process different types of graph theoretic problems such as subgraph matching [5], clique problem [6], Half Hot problem [6], Mutagenesis problem [5], and Tree depth problem[2]. Pucci et al [7], have tested the GNN model on the Movie Lens data set, and pointed out some limitations of Graph Neural Networks when applied to recommender system.…”

Section: Introductionmentioning

confidence: 99%

Graph Neural Network for Minimum Dominating Set

B.¹,

Rani²

2012

IJCA

View full text Add to dashboard Cite

The dominating set concept in graphs has been used in many applications. In large graphs finding the minimum dominating set is difficult. The minimum dominating set problem in graphs seek a set D of minimum number of vertices such that each vertex of the graph is either in D or adjacent to a vertex in D. In a graph on n nodes if there is a single node of degree n-1 then that single node forms a minimum dominating set. In the proposed work, a designed network called Graph Neural Network (GNN) is used to identify the node of degree N-1 in a graph having a single node of degree N-1 as it forms the minimum dominating set in the graph.. The network is simulated for graphs with nodes varying from 5 to 15. The state dimension of the input vectors are analyzed for better convergence. It has been found that the minimum dominating set was correctly identified from 80% to 90% of the graphs when the state dimension was 2 and 3. It has been observed that when the state dimension was 2, the convergence was fast as it requires minimum hidden neurons than other state dimensions. It has also been observed that when the state dimension was greater than 3, convergence requires hours of time and more number of hidden neurons. GNN was able to identify the minimum dominating set in a graph on n vertices which has a single node of degree n-1. General Terms Neural Networks KeywordsMinimum dominating set, Graph neural network, State dimension, Feedforward neural network, Recursive neural network.

show abstract

Computational Capabilities of Graph Neural Networks

Cited by 194 publications

References 29 publications

Unfolding Trees and Symmetrically-Associated Graphs

Unfolding Trees and Symmetrically-Associated Graphs

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

Graph Neural Network for Minimum Dominating Set

Contact Info

Product

Resources

About