between agents that are indirectly connected and agents do not benefit from receiving multiple versions of the same information from the same agent. Such model is suitable for networks with multi-hop relaying where information is forwarded from one node to another [@refz]. We write $i\to j$ to indicate that agent $j$ is reachable by agent $i$ either directly or indirectly. Define the set of agents that $i$ form links with (set of neighbors) as $\mathcal{N}_{i}({\bf g})=\{j|g_{ij}=1\}$, and the set of agents reachable by agent $i$ as $\mathcal{R}_{i}({\bf g})=\{j|i\to j\}$. Throughout the paper, we adopt the following definitions.

**Network component-** a component $\mathcal{C}$ is a set of agents such that $i\to j,\forall i,j\in\mathcal{C}$, and $i\not\to j,\forall i\in\mathcal{C}$ and $j\notin\mathcal{C}$, i.e. two agents in two different components cannot share information.

**Minimally connected component-** a component is minimally connected if each agent $i\in\mathcal{C}$ is connected to each agent $j\in\mathcal{C}$ via a unique path.

Agents in a component share the information they possess and consequently attain “informational" benefits that are captured via a utility function. The utility function of agent $i$ is given by $$u_{i}({\bf g})=f\left(H(X_{i\cup\mathcal{R}_{i}({\bf g})})\right)-\sum_{j\in\mathcal{N}_{i}({\bf g})}c_{ij},\label{eq02}$$ where the function $f(.)$ represents the benefit of agent $i$ from the information it gathers. We 