  In this work, we propose a novel Knowledge Graph Embedding (KGE) strategy,
called M\"{o}biusE, in which the entities and relations are embedded to the
surface of a M\"{o}bius ring. The proposition of such a strategy is inspired by
the classic TorusE, in which the addition of two arbitrary elements is subject
to a modulus operation. In this sense, TorusE naturally guarantees the critical
boundedness of embedding vectors in KGE. However, the nonlinear property of
addition operation on Torus ring is uniquely derived by the modulus operation,
which in some extent restricts the expressiveness of TorusE. As a further
generalization of TorusE, M\"{o}biusE also uses modulus operation to preserve
the closeness of addition operation on it, but the coordinates on M\"{o}bius
ring interacts with each other in the following way: {\em \color{red} any
vector on the surface of a M\"{o}bius ring moves along its parametric trace
will goes to the right opposite direction after a cycle}. Hence, M\"{o}biusE
assumes much more nonlinear representativeness than that of TorusE, and in turn
it generates much more precise embedding results. In our experiments,
M\"{o}biusE outperforms TorusE and other classic embedding strategies in
several key indicators.
