This report addresses agreement problems in networks of dynamic agents in presence of invariant nodes. The network consists of a set of integrator agents which can communicate according to an underlying topology. Invariant nodes are nodes whose dynamics are invariant of their connection to the network. These nodes can be thought of as local leaders, adversaries or intruders trying to break the group consensus or simply nodes of more importance than regular nodes. The convergence of the networks of dynamic agents with presence of invariant nodes has been studied and it has been shown that determination of the steady sate values of regular nodes in presence of invariant nodes results in solving a discrete Dirichlet problem with boundary values given by the invariant nodes.