  Cross-border migration brings economic and cultural impacts to the origin and
destination, and is also a key to reflect the international relations of
related countries. In fact, the migration relationships of countries are
complex and multilateral, but most traditional migration models are bilateral.
Network theories could provide a better description of global migration to show
the structure and statistical characteristics more clearly. Based on the
estimated migration data and disparity filter algorithm, the networks
describing the global multilateral migration relationships has been extracted
among 200 countries over fifty years. The results show that the global
migration networks during 1960-2015 exhibit a clustering and disassortative
feature, implying globalized and multipolarized changes of migration during
these years. The networks were embed into a Poincar\'e disk, yielding a typical
and hierarchical "core-periphery" structure which, associated with angular
density distribution, has been used to describe the "multi-centering" trend
since 1990s. Analysis on correlation and evolution of communities indicates the
stability of most communities yet some structural changes still exist since
1990s, which reflect that the important historical events are contributable to
regional and even global migration patterns.
