Search results for "Graph property"
showing 6 items of 6 documents
A comparison of compatible, finite, and inductive graph properties
1993
Abstract In the theory of hyperedge-replacement grammars and languages, one encounters three types of graph properties that play an important role in proving decidability and structural results. The three types are called compatible, finite, and inductive graph properties. All three of them cover graph properties that are well-behaved with respect to certain operations on hypergraphs. In this paper, we show that the three notions are essentially equivalent. Consequently, three lines of investigation in the theory of hyperedge replacement - so far separated - merge into one.
The Monadic Quantifier Alternation Hierarchy over Grids and Graphs
2002
AbstractThe monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k+1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k+1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrar…
Tree automata, tree decomposition and hyperedge replacement
2005
Recent results concerning efficient solvability of graph problems on graphs with bounded tree-width and decidability of graph properties for hyperedge-replacement graph grammars are systematised by showing how they can be derived from recognisability of corresponding tree classes by finite tree automata, using only well-known techniques from tree-automata theory.
Relations between structure and estimators in networks of dynamical systems
2011
The article main focus is on the identification of a graphical model from time series data associated with different interconnected entities. The time series are modeled as realizations of stochastic processes (representing nodes of a graph) linked together via transfer functions (representing the edges of the graph). Both the cases of non-causal and causal links are considered. By using only the measurements of the node outputs and without assuming any prior knowledge of the network topology, a method is provided to estimate the graph connectivity. In particular, it is proven that the method determines links to be present only between a node and its “kins”, where kins of a node consist of …
Temporal aggregation in chain graph models
2005
The dependence structure of an observed process induced by temporal aggregation of a time evolving hidden spatial phenomenon is addressed. Data are described by means of chain graph models and an algorithm to compute the chain graph resulting from the temporal aggregation of a directed acyclic graph is provided. This chain graph is the best graph which covers the independencies of the resulting process within the chain graph class. A sufficient condition that produces a memory loss of the observed process with respect to its hidden origin is analyzed. Some examples are used for illustrating algorithms and results.
Biased graph walks for RDF graph embeddings
2017
Knowledge Graphs have been recognized as a valuable source for background information in many data mining, information retrieval, natural language processing, and knowledge extraction tasks. However, obtaining a suitable feature vector representation from RDF graphs is a challenging task. In this paper, we extend the RDF2Vec approach, which leverages language modeling techniques for unsupervised feature extraction from sequences of entities. We generate sequences by exploiting local information from graph substructures, harvested by graph walks, and learn latent numerical representations of entities in RDF graphs. We extend the way we compute feature vector representations by comparing twel…