also referred to as a canonical vector. The symbol $\top$ stands for matrix transpose. The operator $\otimes$ denotes the Kronecker product. The operator $|| . ||$ applied to a vector is the standard Euclidean $\mathcal{L}_{2}$ norm, while when applied to matrices stands for the induced $\mathcal{L}_{2}$ norm, which is equal to the spectral radius for symmetric matrices. The cardinality of a set $\mathcal{S}$ is $\left|\mathcal{S}\right|$. Finally, $diag(\mathbf{v})$ denotes the diagonal matrix with its diagonal elements as $\mathbf{v}$. All inequalities involving random variables are to be interpreted almost surely (a.s.).\
**Spectral Graph Theory.** The inter-agent communication network is a simple[^3] undirected graph $G=(V, E)$, where $V$ denotes the set of agents or vertices with cardinality $|V|=N$, and $E$ the set of edges with $|E|=M$. If there exists an edge between agents $i$ and $j$, then $(i,j)\in E$. A path between agents $i$ and $j$ of length $m$ is a sequence ($i=p_{0},p_{1},\cdots,p_{m}=j)$ of vertices, such that $(p_{t}, p_{t+1})\in E$, $0\le t \le m-1$. A graph is connected if there exists a path between all possible agent pairs. The neighborhood of an agent $n$ is given by $\Omega_{n}=\{j \in V|(n,j) \in E\}$. The degree of agent $n$ is given by $d_{n}=|\Omega_{n}|$. The structure 