This paper proposes three methods of the optimal smart meter selection for acting as a data concentrator in the automatic meter reading last mile network. The study explains the reasons why the selected smart meter should also act as a data concentrator, in addition to its basic role. To select the smart meter, either the reliability of communication or the speed of the automatic meter reading process was considered. Graph theory is employed to analyse the last mile network, described as sets of nodes and unreliable links. The frame error ratio was used to assess the unreliability whilst the number of hops was used to describe the speed of the reading process. The input data for the analysis are qualitative parameters determined based on observations in the real, operated last mile networks as well as their typical topological arrangements. The results of the research can be useful in the last mile network migration process, which uses concentrators to the networks without them, or during the process of newer last mile network implementation, where data concentrators are no longer applicable. The efficiency of the proposed methods is assessed measurably.