Entropy of spatial network ensembles

Physical Review. E
Justin P CoonOrestis Georgiou

Abstract

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly in space and links formed independently between pairs of nodes with probability given by a specified function (the "pair connection function") of their mutual distance. We consider the general case where randomness arises in node positions as well as pairwise connections (i.e., for a given pair distance, the corresponding edge state is a random variable). Classical random geometric graph and exponential graph models can be recovered in certain limits. We derive a simple bound for the entropy of a spatial network ensemble and calculate the conditional entropy of an ensemble given the node location distribution for hard and soft (probabilistic) pair connection functions. Under this formalism, we derive the connection function that yields maximum entropy under general constraints. Finally, we apply our analytical framework to study two practical examples: ad hoc wireless networks and the US flight network. Through the study of these examples, we illustrate that both exhibit properties that are in...Continue Reading

References

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Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kartik AnandSimone Severini
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Justin CoonOrestis Georgiou
Mar 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Arda HaluGinestra Bianconi
Apr 15, 2016·Physical Review. E·Carl P Dettmann, Orestis Georgiou

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Citations

Feb 20, 2019·Journal of Translational Medicine·Yaron Ilan

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