Topological weaves are complex entangled structures defined as an embedding of infinitely many simple open curves in the thickened plan. In the case of a doubly periodic structure, the topology is entirely encoded in any generating cell of the infinite diagram, which is a particular link diagram on a torus. However, when studying equivalence classes of doubly periodic weaves, one must consider the infinite number of possibilities to choose a generating cell, namely all the links that lift to equivalent weaves in the universal cover. In this talk, we will introduce a new weaving invariant that describes entanglement on a torus diagram to classify doubly periodic (p,q)-weaves. This is a joint work with Prof. Motoko Kotani and Dr. Mizuki Fukuda.