This paper presents a new circuit theoretical concept based on the principal partition theorem for distributed network management focusing on loops of an information network. To realize a simple network management with the minimum number of local agents, namely the topological degrees of freedom of a graph, a reduced loop agent graph generated by contracting the minimal principal minor is proposed. To investigate the optimal distribution of the loop agents, a theory of tie-set graph is proposed. Considering the total processing load of loop agents, a complexity of a tie-set graph is introduced to obtain the simplest tie-set graph with the minimum complexity. As for the simplest tie-set graph search, an experimental result shows that the computational time depends heavily on the nullity of the original graph. Therefore, a tie-set graph with the smallest nullity is essential for network management. Copyright © 2001 John Wiley & Sons, Ltd.
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