Accurate topology information is crucial to management and application in an active low-voltage distribution network (LVDN). Existing topology identification (TI) methods mostly lack a systematic framework to obtain precise hierarchical relations and consumers' segment locations. Their performances are usually deteriorated by introduction of incomplete and tampered smart meter data. To address the problem of TI with penetration of PV prosumers

non-consumption users

and electricity thieves

a data-driven algorithm is proposed via measurements of nodal voltage magnitude and active power

without any prior network information. Inspired by engineering applications of graph theory knowledge

we cast connection problems of LVDN into the solution of adjacency matrices. Up-down and parallel relations of branches are first identified using active power

based on feature extraction of frequency domain filtering and correlation. Correlation factor analysis is subsequently adopted to assign multiple consumers to specific subnetworks

and then consumers' segments are precisely located by combining regression analysis and association strategy. The proposed algorithm is successfully examined on in a complex LVDN

and results show higher robustness under different scenarios.