A general equation to calculate the node pressure at a junction in a microfluidic network is presented. The node pressure is generated from both the hydrodynamic flow due to the external applied hydraulic pressures and the electrokinetic flow resulted from the applied electric field, Pure electroosmotic flow has a plug-flow profile and pressure flow has a parabolic flow profile. In a first order approximation, these two flows can be treated separately, and the total flow is the sum of the two. An externally applied pressure simply creates a constant offset in the node pressure as long as the flow resistances remain the same. In a nonhomogeneous microfluidic network, where the electrical resistivity or the electroosmotic mobility is not constant everywhere, the differences in electroosmotic flow in various sections of the network will create an electroosmotically induced pressure at the internal nodes. Our theoretical approach can easily be extended to networks with more than one internal node. One prediction of this theory is that any variation in electroosmotic mobility or solution resistivity in different network branches will generate a pressure, and can thus be used as a pump. As an example, we demonstrate electroosmotic pumping in a high-low buffer system.