Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.

During nervous system development, neurons extend axons along well-defined pathways. The current understanding of axon pathfinding is based mainly on chemical signalling. However, growing neurons interact not only chemically but also mechanically with their environment. Here we identify mechanical signals as important regulators of axon pathfinding. In vitro, substrate stiffness determined growth patterns of Xenopus retinal ganglion cell (RGC) axons. In vivo atomic force microscopy revealed striking stiffness gradient patterns in the embryonic brain. RGC axons grew towards the tissue’s softer side, which was reproduced in vitro in the absence of chemical gradients. To test the importance of mechanical signals for axon growth in vivo, we altered brain stiffness, blocked mechanotransduction pharmacologically, and knocked down the mechanosensitive ion channel Piezo1. All treatments resulted in aberrant axonal growth and pathfinding errors, suggesting that local tissue stiffness–read out by mechanosensitive ion channels–is critically involved in instructing neuronal growth in vivo.

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