Shortest Paths in Complex Networks: Structure and Optimization.

Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on several dynamical processes taking place on the network. In addition, several practical situations, such as transit in cities, can benefit by modifying a network so as to reduce the respective shortest paths. In the present work, we addressed the problem of trying to reduce the average shortest path of several theoretical and real-world complex networks by adding a given number of links according to different strategies. More specifically, we considered: placing new links between nodes with relatively low and high degrees; to enhance the degree regularity of the network; preferential attachment according to the degree; linking nodes with relatively low and high betweenness centrality; and linking nodes with relatively low/low, low/high, and high/high accessibilities. Several interesting results have been obtained, including the identification of the accessibility-based strategies as providing the largest reduction of the average shortest path length. Another interesting finding is that, for several types of networks, the degree-based methods tend to provide improvements comparable to those obtained by using the much more computationally expensive betweenness centrality measurement.