In this chapter, the networks of saddle and center, connected parabola saddles with connected hyperbolic and hyperbolic-secant flows are presented, and the switching bifurcations of such networks are discussed through the infinite equilibriums. Parabola saddles are the appearing and switching bifurcations of saddle and center. The third-order saddle is the appearing bifurcation of saddle, center, and saddle. The third-order center is the appearing bifurcation of center, saddle, and center. The parabola saddles on the inflection-source (sink) infinite-equilibriums are the switching bifurcations of a center with a hyperbolic flow and a saddle with a hyperbolic-secant flow. The hyperbolic and circular source-to-sink or sink-to-source on the parabola-source and sink infinite equilibriums are for parabola saddle with saddle and center, respectively. The third-order parabola-saddles on the third-order inflection-source (sink) infinite equilibriums are the switching bifurcations of a hyperbolic flow with a third-order center and a hyperbolic-secant flow with a third-order saddle, respectively.