Series-parallel networks are often used as models for electric circuits. We use series-parallel graphs to represent series-parallel networks. Since there are many different graph representations for a series-parallel network, we are interested in studying maximum matching in different graph representations of a single network. The number of edges in a maximum matching of G is called the edge independence number of G and is denoted by β(G). For a network N, the maximum matching number, β(N), is defined to be max{β (G[N])|[N] is a graph representation for N}, and the minimum matching number, β*(N), is defined to be min{(G[N])|[N] is a graph representation for N}. Since there exist some networks with β (N) - β*(N) ≧ k for any positive integer k, computations of β(N) and β*(N) become significant. In this paper, we present linear time algorithms to compute β(N) and β*(N) for any series-parallel network N.