AVERAGE PATH LENGTH AND AVERAGE FERMAT DISTANCE OF A CLASS OF POLYGON NETWORKS

The average path length of a network serves to elucidate the network's fluency and coherence by providing insights into how efficiently and effectively information or interactions can traverse the network and it is extensively studied in the context of network science. The Fermat distance among three nodes i, j, and k, denoted as f(i,j,k), was defined as the shortest total path length between a node p and nodes i, j, and k. The corresponding average Fermat distance also plays an important role in describing the connectedness of a network. In this paper, we study a class of polygon networks with pseudo-fractal structure and analyze the average path length. Moreover, we derive the average Fermat distance in two ways. Interestingly, we find the ratio of asymptotic average Fermat distance to asymptotic average path length is exactly 3/2 and these metrics grow linearly with the order of the polygon networks.