Characterizing the Diversity of Dynamics in Complex Networks Without Border Effects

The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks have been comprehensively investigated along the last decade in terms of their topological measurements, relatively less attention has been focused on the characterization of the respective dynamics. Introduced recently, the diversity entropy of complex systems can provide valuable information about the respective possible unfolding of dynamics. In the case of self-avoiding random walks, the situation assumed here, the diversity measurement allows one to quantify in how many different places an agent may effectively arrive after a given number of steps from its initial activity. Because this measurement is highly affected by border effects frequently found as a consequence of network sampling, it becomes critical to devise means for sound estimation of the diversity without being affected by this type of artifacts. We describe such an algorithm and illustrate its potential with respect to the characterization of the self-avoiding random walk dynamics in two real-world networks, namely bone canals and air transportation.