We propose a novel solution in differential network analysis to both the network comparison and the classification tasks by introducing the glocal HIM metric for comparing graphs and a graph kernel induced by the HIM measure. The HIM distance is defined as the one-parameter family of product metrics linearly combining the normalised Hamming distance H and the normalised Ipsen-Mikhailov spectral distance IM. The combination of the two components within a single metric allows overcoming their drawbacks and obtaining a measure which is simultaneously global and local. Furthermore, plugging the HIM kernel into a Support Vector Machine gives us a classification algorithm based on the HIM distance. Here we outline the underlying theoretical details of the metric construction, and we present several applications of the HIM distance and the HIM kernel to datasets belonging to different areas, including socioeconomics, neuroscience, oncogenomics and developmental genomics, supporting the adoption of the HIM family as a general analysis tool for information extraction based on a quantitative evaluation of the difference among diverse instances of a complex system. We conclude introducing the Open Source implementation of the HIM metrics provided in the R package nettols and in its web interface ReNette.