In network science, a sparse network has much fewer links than the possible maximum number of links within that network (the opposite is a dense network). The study of sparse networks is a relatively new area primarily stimulated by the study of real networks, such as social and computer networks.[1]
The notion of much fewer links is, of course, colloquial and informal. While a threshold for a particular network may be invented, there is no universal threshold that defines what much fewer actually means. As a result, there is no formal sense of sparsity for any finite network, despite widespread agreement that most empirical networks are indeed sparse. There is, however, a formal sense of sparsity in the case of infinite network models, determined by the behavior of the number of edges (M) and/or the average degree (⟨k⟩) as the number of nodes (N) goes to infinity.[2]