The term "modularity" has several meanings in mathematics.
In graph theory, graph modularity is a score of a proposed set partition. The modularity (or maximum modularity) of a graph is the maximum of this score over all vertex partitions.
In lattice theory, modularity is the property defining a modular lattice.
In arithmetic geometry, modularity of an elliptic curve over 
means that its Hasse-Weil
L-function is the 
-function of a weight-two modular
newform, as asserted by the modularity theorem.
