Network science deals with issues related to the aggregation, processing, and diffusion of information over graphs. While interactions among agents can be studied from the perspective of cluster formations, degrees of connectivity, and small-world effects, it is the possibility of having agents interact dynamically with each other, and influence each other’s behavior, that opens up a plethora of notable possibilities. For example, examination of how local interactions influence global behavior can lead to a broader understanding of how localized interactions in the social sciences, life sciences, and system sciences influence the evolution of the respective networks. In this presentation, we examine the learning behavior of adaptive networked agents over both strongly and weakly-connected graphs. The discussion will reveal some interesting patterns of behavior on how information flows over graphs. In the strongly-connected case, all agents are able to learn the desired true state within the same accuracy level, thus attaining a level of “social equilibrium,” even when the agents are subjected to different noise conditions. In contrast, in the weakly-connected case, a leader-follower relationship develops with some agents dictating the behavior of other agents regardless of the local information clues that are sensed by these other agents. The findings clarify how asymmetries in the exchange of data over graphs can make some agents dependent on other agents. This scenario arises, for example, from intruder attacks by malicious agents, from the presence of stubborn agents, or from failures by critical links.