  Many problems in industry --- and in the social, natural, information, and
medical sciences --- involve discrete data and benefit from approaches from
subjects such as network science, information theory, optimization,
probability, and statistics. The study of networks is concerned explicitly with
connectivity between different entities, and it has become very prominent in
industrial settings, an importance that has intensified amidst the modern data
deluge. In this commentary, we discuss the role of network analysis in
industrial and applied mathematics, and we give several examples of network
science in industry. We focus, in particular, on discussing a
physical-applied-mathematics approach to the study of networks. We also discuss
several of our own collaborations with industry on projects in network
analysis.
