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Summary form only given. Knowledge of internal network behaviour is of fundamental importance for a variety of problems such as routing optimization and anomaly detection. The problem of inferring network characteristics using end-to-end measurements is referred to as network tomography. This paper investigates the multiple-source, multiple-receiver (M-by-N) network tomography problem. We identify the dichotomy of 2-by-2 topology components and show that their consideration is sufficient for solving the general M-by-N problem. We describe a probing methodology and decompose the tomography problem into two stages: a series of generalized likelihood ratio tests that determine the appropriate data aggregation, followed by maximum likelihood estimation.