Phylogenetic networks, both rooted and unrooted, are a versatile and invaluable tool for microbiological research. One of the many open theoretical questions sourrounding such networks is when it is possible to orient the edges of a given unrooted network into a valid rooted network, that is, a network in which all non-root nodes have in-degree one (corresponding to a speciation event) or out-degree one (corresponding to a hybridization event). We give a characterization based on the degree of the input graph, showing that graphs of maximum degree three can be oriented in linear time while orienting graphs that may contain degree-five nodes is NP-complete.