Structural Quality of Service in Large-Scale Networks

ions of networks, called structures, are studied. A structure consists of a set of nodes and a set of lines, such that each line connects two nodes. Lines are considered undirected: if a pair of nodes (u, v) is connected by a line, so is (v, u). A path between a source node u and a destination node v is a set of nodes and lines (u = u0), e1, u1, e2, u2, en−1, un−1, en, (un = v), where each line ei connects the nodes ui−1 and ui. The path length is determined by the number of lines between the source and destination node; in the case above, the path is of length n. The distance between two nodes u and v is written d(u, v) and is equal to the length of the shortest path between u and v. Note that d(u, v) = 0 if and only if u = v. The size of a structure is equal to the number of nodes it contains. The degree of a node is the number of lines joined to it.