The word "capacity" has several meanings in mathematics.
In potential theory, the capacity of a compact set in the complex plane is its logarithmic
capacity, which coincides with its transfinite
diameter. In a network flow, the capacity of
a graph edge is a nonnegative upper
bound on the flow assigned to that graph
edge. The max-flow min-cut theorem
equates the maximum 
-
flow
with the minimum capacity of an 
-
cut.
In information theory, channel capacity is the largest rate at which information can be transmitted with arbitrarily small error, while Shannon capacity is a related graph invariant for zero-error communication. In models of population growth, carrying capacity is the maximum sustainable population of a biological species. The term capacity dimension is also used for a dimension defined by the scaling of finite covers of a metric space.
