  Triply-periodic networks (TPNs), like the well-known gyroid and diamond
network phases, abound in soft matter assemblies, from block copolymers (BCPs),
lyotropic liquid crystals and surfactants to functional architectures in
biology. While TPNs are, in reality, volume-filling patterns of
spatially-varying molecular composition, physical and structural models most
often reduce their structure to lower-dimensional geometric objects: the {\it
2D interfaces} between chemical domains; and the {\it 1D skeletons} that thread
through inter-connected, tubular domains. These lower-dimensional structures
provide a useful basis of comparison to idealized geometries based on
triply-periodic minimal, or constant-mean curvature surfaces, and shed
important light on the spatially heterogeneous packing of molecular
constituents that form the networks. Here, we propose a simple, efficient and
flexible method to extract a 1D skeleton from 3D volume composition data of
self-assembled networks. We apply this method to both self-consistent field
theory predictions as well as experimental electron microtomography
reconstructions of the double-gyroid phase of an ABA triblock copolymer. We
further demonstrate how the analysis of 1D skeleton, 2D inter-domain surfaces,
and combinations therefore, provide physical and structural insight into TPNs,
across multiple length scales. Specifically, we propose and compare simple
measures of {\it network chirality} as well as {\it domain thickness}, and
analyze their spatial and statistical distributions in both ideal (theoretical)
and non-ideal (experimental) double gyroid assemblies.
