Online social network has become a new form of infrastructure for communities in spreading situational information in disasters. Developing effective interventions to improve the network performance of information diffusion is essential for people to rapidly retrieve information in coping with disasters and subsequent disruptions. Existing studies have investigated multiple aspects of online social networks in stationary situations and a separate manner. However, the networks are dynamic and different properties of the networks are co-related in the evolving disaster situations. In particular, disaster events motivate people to communicate online, create and reinforce their connections, and lead to a dynamic reticulation of the online social networks. To understand the relationship among these elements, we proposed an Online Network Reticulation (ONR) framework to examine four modalities (i.e., enactment, activation, reticulation, and network performance) in the evolution of online social networks to analyze the interplays among disruptive events in disasters, user activities, and information diffusion performance on social media. Accordingly, we examine the temporal changes in four elements for characterization of reticulation: activity timing, activity types (post, share, reply), reticulation mechanism (creation of new links versus reinforcement of existing links), and structure of communication instances (self-loop, converging, and reciprocal). Finally, the aggregated effects of network reticulation, using attributed network-embedding approach, are examined in the average latent distance among users as a measure of network performance for information propagation. The application of the proposed framework is demonstrated in a study of network reticulation on Twitter for a built environment disruption event during 2017 Hurricane Harvey in Houston. The results show that the main underlying mechanism of network reticulation in evolving situations was the creation of new links by regular users. The main structure for communication instances was converging, indicating communication instances driven by information-seeking behaviors in the wake of a disruptive event. With the evolution of the network, the proportion of converging structures to self-loop and reciprocal structures did not change significantly, indicating the existence of a scaleinvariance property for network structures. The findings demonstrate the capability of the proposed online network reticulation framework for characterizing the complex relationships between events, activities, and network performance in online social networks during disasters.