Cosma Shalizi says a network is essentially anything which can be represented by a graph: a set of points (also generically called nodes or vertices), connected by links (edges, ties) representing some binary relationship (Graph Theory, Everything Is A Graph)
- that piece has some interesting comparisons of various types of networks/graphs, and their Robust Ness under various kinds of insults/attacks. This theme, of a trade-off between resistance to different kinds of insults, was further explored by John Doyle. Generally speaking, minor, as it were petty, insults are much more common than large ones, which do more harm to the network --- the bigger the problem, the more rarely it turns up. (You're bitten by mosquitoes much more often than by tigers.) The large insults may be improbable, but "improbable events permit themselves the luxury of occuring," as Charlie Chan said. In fact, sooner or latter they're bound to happen: if you wait long enough, the chances of their not happening get arbitrarily small. Doyle goes further, and says that when systems, including networks, are designed to cope with insults below a threshold size as well as possible, the damage done by insults above that size is actually increased. He calls this "highly optimized tolerance," and it seems to offer a choice between constant petty failures, and sporadic but inevitable total breakdowns.