Evolutional Codes: Novel Efficient Graph Data Representation for Mobile Edge Computing

To transmit big graph data emerging from prevalent social networks and biological networks over mobile devices has become challenging nowadays. Since graphs are usually represented by the associated adjacency matrices or graph data structures, dynamic node (vertex) re-ordering to reflect the nodes' real relations (for example, spatial or structural relations) is desirable in practice but impossible for these two existing graph-representation methods. Lately, we proposed a novel evolutional coding technique, which can restructure graph data dynamically, flexibly, and efficiently for transmission among mobile devices. Memory efficiency, in terms of number of memory storage units, is a crucial performance measure for mobile edge computing. To select the optimal graph-representation strategy for arbitrary graph data, we define a new graph-taxonomy metric dependent on the edge density (edges per node) in this work. According to our newly defined graph-taxonomy metric, one can choose the optimal graph-representation solution among the three aforementioned methods in terms of required memory-storage space for any application. Pertinent theorems and proofs for the underlying comparative studies on graph representation are presented in this article.