  Weighted simplicial complexes (WSCs) are powerful tools for describing
weighted cloud data or networks with weighted nodes. In this paper, we propose
a novel approach to study WSCs via the concept of polarization. Polarization of
a WSC allows one to construct a new (unweighted) simplicial complex which
coincides with an object called the mixed wreath product. This new construction
preserves several properties and invariants of the underlying simplicial
complex of a WSC. Our main focus is to analyze WSCs through their underlying
simplicial complexes and mixed wreath products. Combinatorially, we investigate
properties such as vertex-decomposability, shellability, constructibility;
algebraically, we study Betti numbers, associated primes and primary
decompositions of ideals associated to WSCs.
