This paper presents a new analytic model for virus propagation in real networks, based on the eigenvalues of the adjacency matrix. The authors show that the epidemic threshold for a network is closely related to the largest eigenvalue of its adjacency matrix. They propose a general epidemic threshold condition that applies to arbitrary graphs, and demonstrate that their model outperforms previous models in predicting the spread of viruses in real and synthesized networks. The model is shown to be accurate for a variety of network topologies, including homogeneous, BA power-law, star, and infinite power-law graphs. The authors also show that, below the epidemic threshold, the number of infected nodes decays exponentially over time. The model is validated through extensive experiments on real and synthesized graphs, and is shown to be more precise than previous models for special-case graphs. The paper concludes that the epidemic threshold is a critical factor in determining whether a virus will spread in a network, and that the proposed model provides a general and accurate way to predict this threshold.This paper presents a new analytic model for virus propagation in real networks, based on the eigenvalues of the adjacency matrix. The authors show that the epidemic threshold for a network is closely related to the largest eigenvalue of its adjacency matrix. They propose a general epidemic threshold condition that applies to arbitrary graphs, and demonstrate that their model outperforms previous models in predicting the spread of viruses in real and synthesized networks. The model is shown to be accurate for a variety of network topologies, including homogeneous, BA power-law, star, and infinite power-law graphs. The authors also show that, below the epidemic threshold, the number of infected nodes decays exponentially over time. The model is validated through extensive experiments on real and synthesized graphs, and is shown to be more precise than previous models for special-case graphs. The paper concludes that the epidemic threshold is a critical factor in determining whether a virus will spread in a network, and that the proposed model provides a general and accurate way to predict this threshold.