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The continuous increase in big data applications, in number and types, creates new challenges that should be tackled by the green ICT community. Big data is mainly characterized by 4 Vs volume, variety, velocity, and veracity. Each V poses a number of challenges that have implications on the energy efficiency of the underlying networks carrying the big data. Addressing the veracity of the data is a more serious challenge to data scientists, since they need to distinguish between the meaningful data and the dirty data. In this article, we investigate the impact of big data veracity on greening IP by developing a Mixed Integer Linear Programming, MILP, model that encapsulates the distinctive features of veracity. In our analyses, the big data network was greened by cleansing the raw big data before processing and then progressively processing the cleansed big data at strategic locations, dubbed processing nodes, PNs. The PNs are built into the network along the path from the sources to the centralized datacenters. At each PN, the cleansed data was processed and smaller volume of useful information was extracted progressively, thereby, reducing the network power consumption. Furthermore, a backup for the cleansed data was stored in an optimally selected Backup Node, BN. We evaluated the network power saving that can be achieved by a green big data network compared to the classical non-progressive approach. We obtained up to 52 percent network power savings, on average, in the green big data approach compared to the classical approach.