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Readability criteria, such as distance or neighborhood preservation, areoften used to optimize node-link representations of graphs to enable thecomprehension of the underlying data. With few exceptions, graph drawingalgorithms typically optimize one such criterion, usually at the expense ofothers. We propose a layout approach, Graph Drawing via Gradient Descent,$(GD)^2$, that can handle multiple readability criteria. $(GD)^2$ can optimizeany criterion that can be described by a smooth function. If the criterioncannot be captured by a smooth function, a non-smooth function for thecriterion is combined with another smooth function, or auto-differentiationtools are used for the optimization. Our approach is flexible and can be usedto optimize several criteria that have already been considered earlier (e.g.,obtaining ideal edge lengths, stress, neighborhood preservation) as well asother criteria which have not yet been explicitly optimized in such fashion(e.g., vertex resolution, angular resolution, aspect ratio). We providequantitative and qualitative evidence of the effectiveness of $(GD)^2$ withexperimental data and a functional prototype:\url{http://hdc.cs.arizona.edu/~mwli/graph-drawing/}.

Graph Drawing via Gradient Descent, $(GD)^2$