Well, if I remember my graph theory well enough, if A is the adjacency matrix of the graph, each entry of A^n is the number of ways to get between the corresponding nodes in n steps or less. So ...

Yet for every apparent complication to sequence assembly, it has proven fruitful to apply some cousin of de Bruijn graphs to transform a question involving Hamiltonian cycles into a different ...

These issues involve dividing a graph’s vertex set into distinct subsets that optimise specific criteria, such as minimising inter-part edge counts or balancing the sizes of the resulting parts.