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The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear structure in the system. The higher-dimensional analogue is an embedding of a graph onto a multi-dimensional Euclidean space and it was used by scientists to study the multi-relational complexity of ecology. However the research went out of fashion in the 1980s and was not revisited when Network Science recently expressed interests with multi-relational networks known as multiplexes. This paper studies interval graphs from the perspective of Network Science.

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