Named Graphs as a Mechanism for Reasoning About Provenance

Named Graphs is a simple, compatible extension to the RDF abstract syntax that enables statements to be made about RDF graphs. This approach is in contrast to earlier attempts such as RDF reification, or knowledge-base specific extensions including quads and contexts. In this paper we demonstrate the use of Named Graphs and our experiences developing new kinds of semantic web application that build on Named Graphs for digital signatures, provenance, and semantic reasoning. We present a working example based on the Named Graphs for Jena (NG4J) API, from which we developed a semantic version control system for Software Engineering capable of reasoning about Named Graph-based provenance. We go on to discuss the implications of Named Graphs for Description Logics and semantic inference strategies

Quasiperiodic graphs: structural design, scaling and entropic properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

Towards supporting multiple semantics of named graphs using N3 rules

Semantic Web applications often require the partitioning of triples into subgraphs, and then associating them with useful metadata (e.g., provenance). This led to the introduction of RDF datasets, with each RDF dataset comprising a default graph and zero or more named graphs. However, due to differences in RDF implementations, no consensus could be reached on a standard semantics; and a range of different dataset semantics are currently assumed. For an RDF system not be limited to only a subset of online RDF datasets, the system would need to be extended to support different dataset semantics—exactly the problem that eluded consensus before. In this paper, we transpose this problem to Notation3 Logic, an RDF-based rule language that similarly allows citing graphs within RDF documents. We propose a solution where an N3 author can directly indicate the intended semantics of a cited graph— possibly, combining multiple semantics within a single document. We supply an initial set of companion N3 rules, which implement a number of RDF dataset semantics, which allow an N3-compliant system to easily support multiple different semantics

A new intrinsically knotted graph with 22 edges

A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the 13 graphs obtained from $K_7$ by $\nabla Y$ moves are the only intrinsically knotted graphs with 21 edges. In this paper we present the following results: there are exactly three triangle-free intrinsically knotted graphs with 22 edges having at least two vertices of degree 5. Two are the cousins 94 and 110 of the $E_9+e$ family and the third is a previously unknown graph named $M_{11}$. These graphs are shown in Figure 3 and 4. Furthermore, there is no triangle-free intrinsically knotted graph with 22 edges that has a vertex with degree larger than 5

Lombardi Drawings of Graphs

We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.Comment: Expanded version of paper appearing in the 18th International Symposium on Graph Drawing (GD 2010). 13 pages, 7 figure