We study a network of interconnected agents, which are subject to epidemic risks such as those caused by propagating viruses and worms. Each agent can decide whether or not to invest some amount to self-protect and deploy security solutions which decreases the probability of contagion. Borrowing ideas from random graphs theory, we solve explicitly this ’micro’-model and compute the fulfilled expectations equilibria. We are able to compute the network externalities as a function of the parameters of the epidemic. We show that the network externalities have a public part and a private one. As a result of this separation, some counter-intuitive phenomena can occur: there are situations where the incentive to invest in self-protection decreases as the fraction of the population investing in self-protection increases. In a situation where the protection is strong and ensures that the protected agent cannot be harmed by the decision of others, we show that the situation is similar to a free-rider problem. In a situation where the protection is weaker, then we show that the network can exhibit critical mass. We also look at interaction with the security supplier. In the case where security is provided by a monopolist, we show that the monopolist is taking advantage of these positive network externalities by providing a low quality protection.