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A multi-relational graph maintains two or more relations over a vertex set. This article defines an algebra for traversing such graphs that is based on an $n$-ary relational algebra, a concatenative single-relational path algebra, and a tensor-based multi-relational algebra. The presented algebra provides a monoid, automata, and formal language theoretic foundation for the construction of a multi-relational graph traversal engine.
Many, if not most network analysis algorithms have been designed specifically for single-relational networks; that is, networks in which all edges are of the same type. For example, edges may either represent friendship, kinship, or collaboration, bu
Acting on time-critical events by processing ever growing social media or news streams is a major technical challenge. Many of these data sources can be modeled as multi-relational graphs. Continuous queries or techniques to search for rare events th
An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker
Graph Attention Network (GAT) focuses on modelling simple undirected and single relational graph data only. This limits its ability to deal with more general and complex multi-relational graphs that contain entities with directed links of different l
Multi-relational networks are used extensively to structure knowledge. Perhaps the most popular instance, due to the widespread adoption of the Semantic Web, is the Resource Description Framework (RDF). One of the primary purposes of a knowledge netw