  This paper introduces some tools from graph theory and distributed consensus
algorithms to construct an optimal, yet robust, hierarchical information
sharing structure for large-scale decision making and control problems. The
proposed method is motivated by the robustness and optimality of leaf-venation
patterns. We introduce a new class of centrality measures which are built based
on the degree distribution of nodes within network graph. Furthermore, the
proposed measure is used to select the appropriate weight of the corresponding
consensus algorithm. To this end, an implicit hierarchical structure is derived
that control the flow of information in different situations. In addition, the
performance analysis of the proposed measure with respect to other standard
measures is performed to investigate the convergence and asymptotic behavior of
the measure. Gas Transmission Network is served as our test-bed to demonstrate
the applicability and the efficiently of the method.
