1. A device for minimally modifying weights of a minimal set of links, including incrementation and decrementation, to cause a user-definable element in a weighted graph of a network that was not in a shortest path in the graph to appear in a shortest path in the graph after said modification, comprising: a) a receiver for receiving a graph with weights that are real numbers, where the graph includes nodes, links, a source node s, and a destination node t, having an input, and having an output; b) a first shortest-path finder for determining a shortest path from s to t, where shortest path is one for which a sum of the weights of the associated links is minimized, having an input connected to the output of the receiver, and having an output; c) an element selector for selecting a user-definable element in the graph that is not in the shortest path determined by the first shortest-path finder, having an input connected to the output of the first shortest-path finder, and having an output; d) a variable/set setter for setting n=1 and a first set equal to a null set, having an input connected to the output of the element selector, and having an output; e) a path finder for determining a path from s to t that includes the user-definable element, where said path includes a first path from s to the user-definable element and a second path from the user-definable element to t, where the first path and the second path do not have any node in common except a node associated with the user-definable element when the user-definable element is a node, having an input connected to the output of the variable/set setter, and having an output; f) a link finder for identifying links in a path from s to t that include the user-definable element that are not in the shortest path from s to t that does not include the user-definable element, having a first input connected to the output of the first shortest-path finder, having a second input connected to the output of the path finder, a third input, and having an output; g) a decrement checker for determining if decrementing the weights of links would result in a link having a weight less than a first user-definable value and, if so, going to a modified-weight resetter, having an input connected to the output of the link finder, and having an output; h) a link decrementer for minimally decrementing the weights of a minimal number of links identified by the link finder a total amount equal to the sum of the weights of the links from s to t including the user-definable element minus the sum of the weights of the links of the shortest path from s to t that does not include the user-definable element plus a second user-definable value, having a first input connected to the output of the link finder, having a second input connected to the output of the decrement checker, and having an output; i) a link finder/incrementer for determining if the weight-modified path from s to t including the user-definable element is now a shortest path in the graph and, if so, going to a duplicate shortest-path finder, otherwise: A) identifying a link in the shortest path from s to t that does not include the user-definable element that is not in the path from s to t that includes the user-definable element; B) incrementing the weight of the link identified in (i)(A) by an amount equal to a sum of the weights of the weight-modified path from s to t that includes the user-definable element minus a sum of the weights of the links of the shortest path from s to t that does not include the user-definable element plus the second user-definable value; and C) if a path from s to t that does not include the user-definable element is a shortest path in the graph then returning to (i)(A), having a first input connected to the output of the link decrementer, having a second input, having a third input, and having an output; j) the duplicate shortest-path finder for determining if there is a path from s to t that does not include the user-definable element that has an equal sum of weights as the path from s to t that includes the user-definable element as modified then designating such a path as the shortest path from s to t that does not include the user-definable element and going to (i)(A) of the link finder/incrementer, having a first input connected to the output of the link decrementer, having a second input connected to the output of the link finder/incrementer, and having an output; k) a second-set adder for including in a second set, which is indexed to n, the links that were modified, the links in the first set, and the modifications made to said links, having a first input connected to the output of the link decrementer, having a second input connected to the output of the link finder/incrementer, having a third input connected to the output of the duplicate shortest-path finder, and having an output; I) an index incrementer for setting n=n+1, having an input connected to the output of the second-set adder, and having an output; m) the modified-weight resetter for resetting the weights modified in the link decrementer, the link finder/incrementer, and the duplicate shortest-path finder to the corresponding weights in the graph received, having a first input connected to the output of the decrement checker, a second input connected to the output of the link decrementer, a third input connected to the output of the link finder/incrementer, having a fourth input connected to the output of the duplicate shortest-path finder, having a fifth input connected to the output of the index incrementer, and having an output; n) a second shortest-path finder for identifying a shortest path from s to t that does not include the user-definable element, having an input connected to the output of the modified-weight resetter, and having an output; o) a non-common link finder and set updater for identifying a link in the shortest path from s to t that does not include the user-definable element that is not in the path from s to t that includes the user-definable element and adding it to the first set, having a first input connected to the output of the second shortest-path finder, having a second input, and having an output; p) a link incrementer for incrementing the weight of an identified link by an amount equal to the sum of the weights of the path from s to t that includes the user-definable element minus the sum of the weights of the shortest path from s to t that does not include the user-definable element plus the second user-definable value, having an input connected to the output of the non-common link finder and set updater, and having an output; q) a third shortest-path finder for determining the shortest path from s to t, having an input connected to the output of the link incrementer, and having an output; r) an element-in-shortest-path checker for determining if the shortest path from s to t includes the user-definable element and, if so, going to a second duplicate-path checker, otherwise going to the link finder, having an input connected to the output of the third shortest-path finder, and having an output; s) the second duplicate-path checker for determining if a path from s to t that does not include the user-definable element has a sum of weights equal to the sum of weights of the path from s to t that includes the user-definable element and, if so, designating that path the shortest path from s to t that does not include the user-definable element and going to the non-common link finder and set updater, otherwise setting the second set, which is indexed to n, equal to the first set, having an input connected to the output of the element-in-shortest-path checker, and having an output connected to the second input of the non-common link finder and set updater; t) a minimum-links finder for identifying which of the indexed second sets includes the fewest number of links, having an input connected to the output of the second duplicate path checker, and having an output; and u) a network modifier for modifying the network received in accordance with the links and modifications to such links in the identified second set, having an input connected to the output of the minimum-links finder, and having an output.