Recent developments in understanding the structure and dynamics of networks have transformed research in many fields, however, the Geosciences have not benefited much from this new conceptual framework. We focus our study on River deltas, which exhibit complex channel networks, whose connectivity constrains, if not drives, their morphology and evolution. Thus, understanding and quantifying properties of these complex patterns is an essential step to solve the inverse problem of inferring process from form and predict their response in a heavily anthropogenic impacted environment. We proposed a framework based on graph and information theory, which allows us to assess delta channel network properties from a topologic (channel connectivity) and dynamic (flux exchange) perspective [Tejedor et al., 2015a,b], showing via control numerical modelling a relationship between the proposed metrics and the physical properties driving delta dynamics [Tejedor et al., 2016]. This framework also allows us to explore the hypothesis formulation and testing of the existence of a first order principle underlying deltas self-organization to distribute water and sediment to the delta top and the shoreline. Here, we hypothesize that deltas distribute water and sediment fluxes on a given delta topology such as to maximize the diversity of flux delivery to the shoreline. By introducing the concept of nonlocal Entropy Rate (nER) and analyzing ten field deltas in diverse environments and numerically simulated deltas, we present evidence that supports our hypothesis, suggesting that delta networks achieve dynamically accessible maxima of their nER. We discuss how optimal flux distributions in terms of nER, when interpreted in terms of resilience, are configurations that reflect an increased ability to withstand perturbations.