Reverse percolation models for growing real-world networks

• Reverse percolation models for growing real-world networks analyze the overall connectivity of real-world networks after the simultaneous addition of nodes and edges. • We develop elegant analytic models based on generating-function and message-passing approaches for the reverse percolation processes. • We explore network growth scenarios by adding nodes and edges simultaneously under both random and preferential attachment mechanisms. • We evaluate the accuracy of reverse percolation models across multiple real-world networks. • We investigate the generation of scale-free networks through single-step node and edge additions based on the preferential attachment mechanism. Reverse percolation analyzes the overall connectivity of a network after the addition of nodes or edges at predefined probabilities, which parallels the significance and application potential of traditional percolation theory. This paper explores the intersection between reverse percolation and network growth. It discusses the addition of a set of new nodes and edges simultaneously, offering insight into two distinct scenarios: random attachment, where all potential new edges have equal occupation probability, and preferential attachment, where the occupation probability of a potential new edge is proportional to the degree of the original network node it connects to. Reverse percolation analytic models are developed for these scenarios to compute the spanning cluster fraction and the percolation threshold. The accuracy of these models are evaluated across multiple real-world networks. Furthermore, the possibility of generating scale-free networks through single-step node and edge additions based on the preferential attachment mechanism is investigated. The results reveal that the double-unknown generating-function-based model proposed in this paper ensures universal applicability and accurate prediction across both investigated scenarios. In the context of preferential attachment, the simultaneous addition of nodes and edges may always produce a proportion of networks exhibiting scare-free structures. However, irrespective of the emergence of scale-free properties, the connectivity status of these networks can be effectively predicted using the proposed reverse percolation model.