Effect of edge pruning on structural controllability and observability of complex networks

A route pruning algorithm for an automated geographic location graph construction

Automated construction of location graphs is instrumental but challenging, particularly in logistics optimisation problems and agent-based movement simulations. Hence, we propose an algorithm for automated construction of location graphs, in which vertices correspond to geographic locations of interest and edges to direct travelling routes between them. Our approach involves two steps. In the first step, we use a routing service to compute distances between all pairs of L locations, resulting in a complete graph. In the second step, we prune this graph by removing edges corresponding to indirect routes, identified using the triangle inequality. The computational complexity of this second step is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr{O}(L^3)$$\end{document}O(L3), which enables the computation of location graphs for all towns and cities on the road network of an entire continent. To illustrate the utility of our algorithm in an application, we constructed location graphs for four regions of different size and road infrastructures and compared them to manually created ground truths. Our algorithm simultaneously achieved precision and recall values around 0.9 for a wide range of the single hyperparameter, suggesting that it is a valid approach to create large location graphs for which a manual creation is infeasible.

Dilations and degeneracy in network controllability

Network controllability asserts a perspective that the structure—the location of edges that connect nodes—of the network contains important information about fundamental characteristics of our ability to change the behavior that evolves on these networks. It can be used, for example, to determine the parts of the system that when influenced by outside controlling signals, can ultimately steer the behavior of the entire network. One of the challenges in utilizing the ideas from network controllability on real systems is that there is typically more than one potential solution (often many) suggested by the topology of the graph that perform equally well. Picking a single candidate from this degenerate solution set over others should be properly motivated, however, to-date our understanding of how these different options are related has been limited. In this work, we operationalize the existing notion of a dilation into a framework that provides clarity on the source of this control degeneracy and further elucidates many of the existing results surrounding degeneracy in the literature.

Effect of Fixed-Density Thresholding on Structural Brain Networks: A Demonstration in Cerebral Small Vessel Disease

A popular solution to control for edge density variability in structural brain network analysis is to threshold the networks to a fixed density across all subjects. However, it remains unclear how this type of thresholding affects the basic network architecture in terms of edge weights, hub location, and hub connectivity and, especially, how it affects the sensitivity to detect disease-related abnormalities. We investigated these two questions in a cohort of patients with cerebral small vessel disease and age-matched controls. Brain networks were reconstructed from diffusion magnetic resonance imaging data using deterministic fiber tractography. Networks were thresholded to a fixed density by removing edges with the lowest number of streamlines. We compared edge length (mm), fractional anisotropy (FA), proportion of hub connections, and hub location between the unthresholded and the thresholded networks of each subject. Moreover, we compared weighted graph measures of global and local connectivity obtained from the (un)thresholded networks between patients and controls. We performed these analyses over a range of densities (2-20%). Results indicate that fixed-density thresholding disproportionally removes edges composed of long streamlines, but is independent of FA. The edges removed were not preferentially connected to hub or nonhub nodes. Over half of the original hubs were reproducible when networks were thresholded to a density ≥10%. Furthermore, the between-group differences in graph measures observed in the unthresholded network remained present after thresholding, irrespective of the chosen density. We therefore conclude that moderate fixed-density thresholds can successfully be applied to control for the effects of density in structural brain network analysis.