Motivation: New antigen microarray technology enables parallel recording of antibody reactivities with hundreds of antigens. Such data affords system level analysis of the immune system's organization using methods and approaches from network theory. Here we measured the reactivity of 290 antigens (for both the IgG and IgM isotypes) of 10 healthy mothers and their term newborns. We constructed antigen correlation networks (or immune networks) whose nodes are the antigens and the edges are the antigen-antigen reactivity correlations, and we also computed their corresponding minimum spanning trees (MST) - maximal information reduced sub-graphs. We quantify the network organization (topology) in terms of the network theory divergence rate measure and rank the antigen importance in the full antigen correlation networks by the eigen-value centrality measure. This analysis makes possible the characterization and comparison of the IgG and IgM immune networks at birth (newborns) and adulthood (mothers) in terms of topology and node importance. Results: Comparison of the immune network topology at birth and adulthood revealed partial conservation of the IgG immune network topology, and significant reorganization of the IgM immune networks. Inspection of the antigen importance revealed some dominant (in terms of high centrality) antigens in the IgG and IgM networks at birth, which retain their importance at adulthood.