Checking bisimilarity for attributed graph transformation

Borrowed context graph transformation is a technique developed by Ehrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.Postprint (published version

Symbolic Attributed Graphs for Attributed Graph Transformation

In this paper we present a new approach to deal with attributed graphs and attributed graph transformation. This approach is based on working with what we call symbolic graphs, which are graphs labelled with variables together with a formula that constrains the possible values that we may assign to these variables. In particular, in this paper we will compare in detail this new approach with the standard approach to attributed graph transformation

Graph attribution through sub-graphs

We offer an alternative to the standard formalisation of attributed graphs. We propose to represent an attributed graph as a graph with a marked sub-graph, in which the sub-graph represents the data domain, rather than as a tuple of graph and algebra. This is a general construction which can be shown to preserve adhesiveness of categories; it has the advantage of uniformity and gives more flexibility in defining data abstractions. We show equivalence of our formalisation with the standard one, under a suitable encoding of algebras as graphs

A simple yet effective baseline for non-attributed graph classification

Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation learning on graphs in general. As the developed methodologies become more sophisticated, it is important to understand which components of the increasingly complex methods are necessary or most effective. As a first step, we develop a simple yet meaningful graph representation, and explore its effectiveness in graph classification. We test our baseline representation for the graph classification task on a range of graph datasets. Interestingly, this simple representation achieves similar performance as the state-of-the-art graph kernels and graph neural networks for non-attributed graph classification. Its performance on classifying attributed graphs is slightly weaker as it does not incorporate attributes. However, given its simplicity and efficiency, we believe that it still serves as an effective baseline for attributed graph classification. Our graph representation is efficient (linear-time) to compute. We also provide a simple connection with the graph neural networks. Note that these observations are only for the task of graph classification while existing methods are often designed for a broader scope including node embedding and link prediction. The results are also likely biased due to the limited amount of benchmark datasets available. Nevertheless, the good performance of our simple baseline calls for the development of new, more comprehensive benchmark datasets so as to better evaluate and analyze different graph learning methods. Furthermore, given the computational efficiency of our graph summary, we believe that it is a good candidate as a baseline method for future graph classification (or even other graph learning) studies.Comment: 13 pages. Shorter version appears at 2019 ICLR Workshop: Representation Learning on Graphs and Manifolds. arXiv admin note: text overlap with arXiv:1810.00826 by other author

Automated reasoning for attributed graph properties

Graphs are ubiquitous in computer science. Moreover, in various application fields, graphs are equipped with attributes to express additional information such as names of entities or weights of relationships. Due to the pervasiveness of attributed graphs, it is highly important to have the means to express properties on attributed graphs to strengthen modeling capabilities and to enable analysis. Firstly, we introduce a new logic of attributed graph properties, where the graph part and attribution part are neatly separated. The graph part is equivalent to first-order logic on graphs as introduced by Courcelle. It employs graph morphisms to allow the specification of complex graph patterns. The attribution part is added to this graph part by reverting to the symbolic approach to graph attribution, where attributes are represented symbolically by variables whose possible values are specified by a set of constraints making use of algebraic specifications. Secondly, we extend our refutationally complete tableau-based reasoning method as well as our symbolic model generation approach for graph properties to attributed graph properties. Due to the new logic mentioned above, neatly separating the graph and attribution parts, and the categorical constructions employed only on a more abstract level, we can leave the graph part of the algorithms seemingly unchanged. For the integration of the attribution part into the algorithms, we use an oracle, allowing for flexible adoption of different available SMT solvers in the actual implementation. Finally, our automated reasoning approach for attributed graph properties is implemented in the tool AutoGraph integrating in particular the SMT solver Z3 for the attribute part of the properties. We motivate and illustrate our work with a particular application scenario on graph database query validation.Peer ReviewedPostprint (author's final draft

Attributed Graph Classification via Deep Graph Convolutional Neural Networks

From social networks to biological networks, graphs are a natural way to represent a diverse set of real-world data. This research presents attributed graph convolutional neural network with a pooling layer (AGCP for short), a novel end-to-end deep neural network model which captures the higher-order latent attributes of weighted, labeled, undirected, attributed graphs of arbitrary size. The architecture of AGCP is an efficient variant of convolutional neural network (CNN) and has a linear filter function that convolves over the fixed topological structure of a graph to learn local and global attributes of the graph. Convolution is followed by a pooling layer that coarsens the graph while preserving the global structure of the original input graph using information gain. On the other hand, advances in high throughput technologies for next-generation sequencing have enabled machine learning research to acquire and extract knowledge from biological networks. We apply AGCP on three bioinformatics networks, ENZYMES, D&D, and GINA a graph dataset of gene interaction networks with genomic mutation attributes as the attributes of the vertices. In several experiments on these datasets, we demonstrate that AGCP yields better results in terms of classification accuracy relative to the previously proposed models by a considerable margin

Client-Driven Content Extraction Associated with Table

The goal of the project is to extract content within table in document images based on learnt patterns. Real-world users i.e., clients first provide a set of key fields within the table which they think are important. These are first used to represent the graph where nodes are labelled with semantics including other features and edges are attributed with relations. Attributed relational graph (ARG) is then employed to mine similar graphs from a document image. Each mined graph will represent an item within the table, and hence a set of such graphs will compose a table. We have validated the concept by using a real-world industrial problem