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

Characterizing the Diversity of Dynamics in Complex Networks Without Border Effects