Spatial networks such as that of the U.S. power grid are particularly vulnerable to collapse as failure at certain junctures can affect a much wider portion of the system, according to a U.S.-Israeli mathematical study of such networks. "Whenever you have such dependencies in the system, failure in one place leads to failure in another place, which cascades into collapse," said study co-author Shlomo Havlin of Israel's Bar-Ilan University.

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