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A theory of tie‐set graph and its application to information network management

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.