As “ideal types” of coordination 

(that is, getting things done through groups) we often hear about Networks as polar opposites of Hierarchy.  Networks are flat, egalitarian, flexible, and emergent, while Hierarchy is vertical, oligarchic, rigid, and prescribed by the powers-that-be.   The two forms are not so much locked in a death struggle for dominance, however, as they are co-existing at the same time in a complex overlay.

Looking for a concrete example?  Consider the regime of Saddam Hussein, up to and including the US-Iraq war beginning in 2003.  A 5 minute video from Slate magazine  reveals how social networks ran alongside the formal government structure, and how US forces used network analysis to track down and capture Saddam.

Abstracting away from Iraq, there are some general principles of Networks vs. Hierarchy that come through loud and clear from this example. 

1. do not confuse networks of influence, knowledge, power with a formal organization chart ... they may overlap, but are of great interest where different.
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2. the inner circle takes care of its own as shown in Art Kleiner’s, Who Really Matters: The Core Group Theory of Power, Privilege, and Success.  
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3. personal networks in some cases may be even stronger than the formal ones (e.g. secrets, deep loyalties, status markers)
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4. from Saddam's POV, Weak Ties (to a wider circle) may bring fresh non-redundant info, but Strong Ties (four intertwined families from Tikrit, with long shared history) are your fallback under stress
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5. from the US Intel / Army POV, the key was creating a "bridge" to the mystery "Fat Man," converting him to a Weak Tie for the US forces, while this bodyguard remained a Strong Tie to Saddam
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Jumping now to a very different context, the combination of Weak and Strong Ties is the same way radical Innovation works.   See the research of Harvard Business School professor Lee Fleming, using network structure (graph theory) to understand the productivity of R&D or Open Sourcing for breakthrough innovation. [link].  The Weak Tie brings in the radical new ideas, but the strong ties of existing "cluster" of researchers allows in-depth testing, vetting, development of an idea, and fast diffusion within the cluster.  In Fleming's argument, you need both the Weak Tie and the Cluster.   Either one alone will not deliver the breakthrough, you need both.