  In this paper, we propose a new type of graph, denoted as "embedded-graph",
and its theory, which employs a distributed representation to describe the
relations on the graph edges. Embedded-graphs can express linguistic and
complicated relations, which cannot be expressed by the existing edge-graphs or
weighted-graphs. We introduce the mathematical definition of embedded-graph,
translation, edge distance, and graph similarity. We can transform an
embedded-graph into a weighted-graph and a weighted-graph into an edge-graph by
the translation method and by threshold calculation, respectively. The edge
distance of an embedded-graph is a distance based on the components of a target
vector, and it is calculated through cosine similarity with the target vector.
The graph similarity is obtained considering the relations with linguistic
complexity. In addition, we provide some examples and data structures for
embedded-graphs in this paper.
