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The vulnerability of a system expresses the behavior of a system confronted with the disturbances generated by natural disasters, adverse weather conditions, technical failures, human errors, sabotage, terrorism and acts of war. These are all scenarios which imply damages over large areas. In this approach, robustness is defined as the capacity of the network to support random hazard experiences. Today, a generally accepted approach to the quantification of vulnerability is made in terms of scale-free networks, because these particular networks have a high capability of conserving their robustness, if a well defined fraction of nodes are highly connected, without the network being over-connected. One way of increasing power grid robustness can be achieved by adding new electric lines between the existing nodes. Our paper suggests an algebraic method of computing optimal enlargement variants and, in the line of our earlier studies on network vulnerability, our purpose is to achieve a robust network, starting from non-robust networks to the nearest free-scale, robust network.

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