Vulnerability analysis of multipolar networks after structural damages

A method to obtain informative estimates of functionality changes in a multistock network system after possible damages has been proposed. Within the framework of the transmission model of single-commodity flow, the authors study the set of achievable flow vectors satisfying the standard conditions of conservation and constraints on the flows along arcs. To analyze the initial state of the system, for each stock arc, the maximum flow has been calculated separately and independently of the flow value across the remaining stock arcs. The corresponding minimal cut separates this stock vertex from the source. All arcs of the found minimal cut are removed model-wisely and in the network which is damaged in this way, the possibilities of transmission flows to other stock vertices have been estimated. The maximum flows for the vertex have been calculated and compared with their initial values. Estimates of losses have been compared for various minimal cuts. Influences of these structural damages have been constructed for all stock vertices. The vertices' aggregated characteristics of the structural damage effect have been calculated.