There are essentially four points that Dr. Chebotarev's raises in [1]. Point 1. Chebotarev claims that Lemma 2 is not correct as stated and gives a counter example consisting of a simple directed tree. This counterexample points out two issues with the lemma as stated. The second portion of Lemma 2, referring to the case in which there are c components, only applies to graphs in which there are disjoint components of the graph (no edges between the components). This is clear from the proof of this fact (which simply consists of separating the nodes so that the Laplacian is block diagonal, implying a disjoint set of nodes), but is ambiguous in the statement of the lemma.

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations.