A Directed Graphs

A.2 Proof of Theorem 1 Before showing properties of W defined by (3), we provide two lemmas as follows. Referring to Theorem 1.6 of [32], we have the following result for a sequence of random matrices. One-peer undirected graphs generated in Alg. 2 with s = 3 and u = 1, . . . From the node's perspective, an equivalent version of Alg. 2 is presented in Alg. 4. In the remainder In Alg. 4, we compute This yields the equivalence between Alg.2 and Alg. 4 for the case of v We first provide the following three lemmas. Averaging the above equations yields the result.