The social science of networks is rich in theory and findings on the effect of structure and topology on performance and behavior. Structural holes, weak ties, small worlds, and scale free graphs are examples of network positions or topologies that are frequently studied. The empirical evidence for topological effects has been surprisingly mixed. We argue that these contradictory results occur because they reflect an important property of organizations, that is, their fragility. We analyze fragility through a agent-based simulation that begins with the broader observation that organizations are fragile because they are social communities. In our approach, since the "social" precedes the "structural," it is not surprising that efforts at organizational design often rely upon such concepts as "socialization" (that is creating homophily) or "teams" (that is creating cohesion). These mechanisms, that is, homophily or cohesion, generate structures that can thwart, or promote, subsequent advantages to an organization. We identify a "sweet spot" where the tendency towards homophily and to cohesion is just "right," creating a structure that facilitates knowledge sharing. In the economics literature on organizational design, this coupling of two mechanisms to generate an "additional supra" effect is an example of complementarities. We analyze the effects of these two mechanisms through a sociological simulation that we call the "knowledge transfer game." To illustrate these ideas, we will draw from empirical studies on auto productivity, microfinance, and restaurants. [Co-authors: Jerry Kim, Jae-Suk Yang].