A visual diagram of inter-connectedness

Mark Thoma of Economist's View posts this useful diagram that visually captures how an inter-connected entity can affect the network of entities connected to it. Imagine each entity in such a network functioning as nodes. If one node in the network malfunctions, then each spoke connected to it is affected, and if these in turn function as nodes themselves to other spokes, it doesn't take long before the malfunction of one node short-circuits the entire system.

Prof. Thoma says: Since measures of connectedness exist, and I presume physicists also have such measures (of complexity), I'm wondering if financial market regulators should start developing measures along these lines. Can we measure the connectedness of financial institutions econometrically? If so, can we also follow along the lines of the Hirfandahl index for monopoly power and develop guidelines for when a firm is too interconnected with other firms, so interconnected that it's failure threatens the overall system? Couldn't we then "break-up" the firms the way we do monopolies, "disconnect" the firm until it's failure wouldn't be so devastating?

As pointed out above, size alone isn't the key feature, the degree of connectedness (complexity) is also important, and regulators - as far as I know - don't have good empirical tools for assessing this aspect of financial markets.

Perhaps a way to easily "disconnect" firms is for regulators to emulate what competent electricians have been doing all along - require that firms create alternate connections along crucial nodes in the circuit. Might just add more complexity in the case of financial firms though.