‘Digging deeper into networks’ shows that to capture the more subtle structure of networks one has to find measures that describe the surroundings of a node — degree distribution is not enough. Characteristics and measurements discussed are assortative and disassortative networks, ego networks, clustering coefficient, betweenness centrality of a node, communities or modules in networks, motifs, and edge betweenness. Although a simplification, the graph representation is still capable of capturing many relevant features of a system. The graph provides plenty of information and more details arise when more complex measurements are performed. Generally, real-world networks deviate from their random counterparts, suggesting the existence of some kind of built-in order and self-organization.