Further Towards Unambiguous Edge Bundling: Investigating Power-Confluent Drawings for Network Visualization.

Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and short-circuit problems, and solve both by modifying the routing graph to retain the hierarchical structure of power groups. We also classify the exact type of confluent drawings that the algorithm can produce as 'power-confluent', and prove that it is a subclass of the previously studied 'strict confluent' drawing. A description and source code of our implementation is also provided, which additionally includes an improved method for power graph construction.

Predation risk influences food-web structure by constraining species diet choice.

The foraging behaviour of species determines their diet and, therefore, also emergent food-web structure. Optimal foraging theory (OFT) has previously been applied to understand the emergence of food-web structure through a consumer-centric consideration of diet choice. However, the resource-centric viewpoint, where species adjust their behaviour to reduce the risk of predation, has not been considered. We develop a mechanistic model that merges metabolic theory with OFT to incorporate the effect of predation risk on diet choice to assemble food webs. This 'predation-risk-compromise' (PR) model better captures the nestedness and modularity of empirical food webs relative to the classical optimal foraging model. Specifically, compared with optimal foraging alone, risk-mitigated foraging leads to more-nested but less-modular webs by broadening the diet of consumers at intermediate trophic levels. Thus, predation risk significantly affects food-web structure by constraining species' ability to forage optimally, and needs to be considered in future work.

Graph Drawing by Stochastic Gradient Descent.

A popular method of force-directed graph drawing is multidimensional scaling using graph-theoretic distances as input. We present an algorithm to minimize its energy function, known as stress, by using stochastic gradient descent (SGD) to move a single pair of vertices at a time. Our results show that SGD can reach lower stress levels faster and more consistently than majorization, without needing help from a good initialization. We then show how the unique properties of SGD make it easier to produce constrained layouts than previous approaches. We also show how SGD can be directly applied within the sparse stress approximation of Ortmann et al. [1], making the algorithm scalable up to large graphs.