Inhibiting the main protease of SARS-CoV-2 is of great interest in tackling the COVID-19 pandemic caused by the virus. Most efforts have been centred on inhibiting the binding site of the enzyme. However, considering allosteric sites, distant from the active or orthosteric site, broadens the search space for drug candidates and confers the advantages of allosteric drug targeting. Here, we report the allosteric communication pathways in the main protease dimer by using two novel fully atomistic graph-theoretical methods: Bond-to-bond propensity, which has been previously successful in identifying allosteric sites in extensive benchmark data sets without a priori knowledge, and Markov transient analysis, which has previously aided in finding novel drug targets in catalytic protein families. Using statistical bootstrapping, we score the highest ranking sites against random sites at similar distances, and we identify four statistically significant putative allosteric sites as good candidates for alternative drug targeting.