a new algorithm for counting independent motifs in probabilistic networks biological networks provide great potential to understand how cells function motifs are topological patterns which are repeated frequently in a specific network network motifs are key structures through which biological networks operate however counting independent ie nonoverlapping instances of a specific motif remains to be a computationally hard problem motif counting problem becomes computationally even harder for biological networks as biological interactions are uncertain events the main challenge behind this problem is that different embeddings of a given motif in a network can share edges such edges can create complex computational dependencies between different instances of the given motif when considering uncertainty of those edges in this paper we develop a novel algorithm for counting independent instances of a specific motif topology in probabilistic biological networks we present a novel mathematical model to capture the dependency between each embedding and all the other embeddings which it overlaps with we prove the correctness of this model we evaluate our model on real and synthetic networks with different probability and topology models as well as reasonable range of network sizes our results demonstrate that our method counts nonoverlapping embeddings in practical time for a broad range of networks