Towards a navigational logic for graphical structures

One of the main advantages of the Logic of Nested Conditions, defined by Habel and Pennemann, for reasoning about graphs, is its generality: this logic can be used in the framework of many classes of graphs and graphical structures. It is enough that the category of these structures satisfies certain basic conditions. In a previous paper [14], we extended this logic to be able to deal with graph properties including paths, but this extension was only defined for the category of untyped directed graphs. In addition it seemed difficult to talk about paths abstractly, that is, independently of the given category of graphical structures. In this paper we approach this problem. In particular, given an arbitrary category of graphical structures, we assume that for every object of this category there is an associated edge relation that can be used to define a path relation. Moreover, we consider that edges have some kind of labels and paths can be specified by associating them to a set of label sequences. Then, after the presentation of that general framework, we show how it can be applied to several classes of graphs. Moreover, we present a set of sound inference rules for reasoning in the logic.Peer ReviewedPostprint (author's final draft

Generalised compositionality in graph transformation

We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph passing between components, meaning that components may “learn” and “forget” subgraphs through communication with other components. Secondly, composition is no longer binary; instead, it can be repeated for an arbitrary number of components

Tractable Optimization Problems through Hypergraph-Based Structural Restrictions

Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal solution is an NP-hard problem in general; yet, when restricted over classes of instances whose constraint interactions can be modelled via (nearly-)acyclic graphs, this problem is known to be solvable in polynomial time. In this paper, larger classes of tractable instances are singled out, by discussing solution approaches based on exploiting hypergraph acyclicity and, more generally, structural decomposition methods, such as (hyper)tree decompositions

Spectral Graph Forge: Graph Generation Targeting Modularity

Community structure is an important property that captures inhomogeneities common in large networks, and modularity is one of the most widely used metrics for such community structure. In this paper, we introduce a principled methodology, the Spectral Graph Forge, for generating random graphs that preserves community structure from a real network of interest, in terms of modularity. Our approach leverages the fact that the spectral structure of matrix representations of a graph encodes global information about community structure. The Spectral Graph Forge uses a low-rank approximation of the modularity matrix to generate synthetic graphs that match a target modularity within user-selectable degree of accuracy, while allowing other aspects of structure to vary. We show that the Spectral Graph Forge outperforms state-of-the-art techniques in terms of accuracy in targeting the modularity and randomness of the realizations, while also preserving other local structural properties and node attributes. We discuss extensions of the Spectral Graph Forge to target other properties beyond modularity, and its applications to anonymization

Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories

Application conditions for rules and constraints for graphs are well-known in the theory of graph transformation and have been extended already to M-adhesive transformation systems. According to the literature we distinguish between two kinds of satisfaction for constraints, called general and initial satisfaction of constraints, where initial satisfaction is defined for constraints over an initial object of the base category. Unfortunately, the standard definition of general satisfaction is not compatible with negation in contrast to initial satisfaction. Based on the well-known restriction of objects along type morphisms, we study in this paper restriction and amalgamation of application conditions and constraints together with their solutions. In our main result, we show compatibility of initial satisfaction for positive constraints with restriction and amalgamation, while general satisfaction fails in general. Our main result is based on the compatibility of composition via pushouts with restriction, which is ensured by the horizontal van Kampen property in addition to the vertical one that is generally satisfied in M-adhesive categories.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

A graph-semantics of business configurations

In this paper we give graph-semantics to a fundamental part of the semantics of the service modeling language SRML. To achieve this goal we develop a new graph transformation system for what we call 2-level symbolic graphs. These kind of graphs extend symbolic graphs with a simple 2-level hierarchy that can be generalized to arbitrary hierarchies. We formalize the semantics using this new graph transformation system using a simple example of a trip booking agent.Postprint (published version