The escape difficulty measure will provide us with information about the direct neighborhood of the node.
The second algorithmic measure which we use is the escape difficulty.
They also proposed two new measures of network navigability based on a random walk procedure: random walk discovery and escape difficulty.
We also propose two new measures of network navigability based on a random walk procedure: random walk discovery and escape difficulty.
However, it goes through rather large variations, especially the peak between 1925 and 1930, when the value of the average escape difficulty was over 11, so we cannot claim that the trend is very clear.
Another measure of navigability which we propose in this paper is the escape difficulty, where we check how many steps need to be performed by a random walker to leave the 3-neighborhood of n i.
The results are reported in Fig. 10, where we observe a downward-sloping trend in the average escape difficulty, whose values become smaller with time, passing from 8.37 to 5.93 between 1890 and 2000.
Indeed, this is what we find by launching the escape difficulty procedure for each node of the maritime network and by taking the average of all the scores (just as in the case of random walk discovery, we iterate the algorithm 100 times for each node).
If the score of the escape difficulty is low, we can suspect that the node lies in a sparse and highly connected neighborhood (formally, in a part of the graph with good expansion), such as a tree, or a forest, rather than a collection of weakly connected clusters.
The random walk discovery measures the ease of exploration of a network in a given number of steps, while the escape difficulty tells us how hard is it to leave a 3-neighborhood of a given node, and therefore provides us with valuable insights about the global network structure.
