Biomimetic nanocomposites from cellulose and other nanofibers are attractive as resource-conscious alternative to many current load bearing, charge transporting, ion-selective, and optically-active materials. These composites contain a superposition of order and disorder, which makes them difficult to design optimize. Similar pairing or non-randomness and stochasticity is also present in high-performance load-bearing, mass-transporting, ion-selective, and optically-active biomaterials. For all of them, the desirable combinations of hard-to-reach properties is attained by intertwining structural patterns at different scales. However, both for Nature- and man-designed materials the large degree of stochasticity make it difficult to describe their structure because the current methodologies developed for crystals, quasicrystals, and glasses become inapplicable. A series of recent studies shows that this problem relevant for multiple disciplines can be addressed using graph theory (GT) and topometric materials design. Graphs, i.e. sets of nodes and edges, are able to capture both ordered and disordered components of complex and hierarchically organized materials. We found that GT descriptors extracted from electron microscopy images can quantify and accurately identify the structural pattern with short-, medium-, and long-range regularities. Taking examples of fibrous nanocomposites based on cellulose nanocrystals, metal nanowires, gold nanodendrites and aramid nanofibers, the utility and universality of this approach is demonstrated. Topometric relations, i.e. when physical property is calculated using both topological and metric parameters, were developed for nanowire coatings, nanofibrous battery cathodes and chiroptical nanodendrites. GT methods can be applied to man-made and evolution-optimized biomaterials enabling accurate replication of biological templates to exceed the performance of biological prototypes. The controllable combination of order and disorder opens the door to scalable biomimetics removing a critical bottleneck in many modern technologies.