  This study develops an original and innovative matrix representation with
respect to the information flow for networked multi-agent system. To begin
with, the general concepts of the edge Laplacian of digraph are proposed with
its algebraic properties. Benefit from this novel graph-theoretic tool, we can
build a bridge between the consensus problem and the edge agreement problem; we
also show that the edge Laplacian sheds a new light on solving the leaderless
consensus problem. Based on the edge agreement framework, the technical
challenges caused by unknown but bounded disturbances and inherently nonlinear
dynamics can be well handled. In particular, we design an integrated procedure
for a new robust consensus protocol that is based on a blend of algebraic graph
theory and the newly developed cyclic-small-gain theorem. Besides, to highlight
the intricate relationship between the original graph and cyclic-small-gain
theorem, the concept of edge-interconnection graph is introduced for the first
time. Finally, simulation results are provided to verify the theoretical
analysis.
