possessed by each agent $i$ is $H(X_{i})$ (no information is shared).

See Appendix C.

From the above Lemma, we can see that three factors affect the connectivity of a network: the link cost, the amount of information possessed by each agent, and the redundancies among the agents’ information. Based on the result of Lemma 1, we define three regions for the connectivity of the NE networks based on the link cost as follows:

-   *Connected agents region* ($\mathcal{K}_{C}$): A network with an entropic vector $\overrightarrow{{\bf H}}$ has a single component when the link cost is $c\leq c_{l}$.

-   *Isolated agents region* ($\mathcal{K}_{I}$): The network has $N$ components when the link cost is $c\geq c_{u}$.

-   *Mixed region* ($\mathcal{K}_{M}$): Depending on the entropic vector, the network can have different number of components ranging from 1 to $N$ when the link cost is $c_{l}\leq c\leq c_{u}$.

While the connectivity regions describe the impact of link cost on network topology, they also have informational significance. For instance, the amount of information possessed by any agent in the $\mathcal{K}_{C}$ region is $H(\mathcal{X})$, while in the $\mathcal{K}_{I}$ region, no agent $i$ gathers any extra information other than its own intrinsic information $H(X_{i})$. On the other 