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The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept of mutual conditional independence relationship among elements of an independent set of a Markov network. We first prove that the mutual conditional independence property holds within the elements of a maximal independent set afterwards we prove equivalencearXiv:1603.03733v1 fatcat:qghhwy77fvfvjpatvqjumfbdf4