This paper investigates the spatiotemporal characteristics and predictability of the emerging modern traffic behavior, ridesourcing. We collect a comprehensive data set of Didi ridesourcing cars on a large geographical scale of a capital city in China, including both the temporal order information and the GPS-recorded spatial trajectories. To extract the features of this kind of traffic behavior, we construct a large-scale network by considering every traffic flow of the orders. Therein, a driver consecutively visiting different regions of the city connects the relationship of these sites. The weighted ridesourcing network shows a consistency of the distribution of trip orders and the Clark model for population distribution. The network also has spatial and temporal features with power laws, sometimes with exponential truncations and log-normal distributions. Furthermore, we propose a general analytical method to quantify the predictability of this kind of behavior by calculating the entropy at a collective level, which can be extended to quantify other traffic behaviors. Finally, by considering the traffic congestion factor, we propose a better neural network based model for predicting dwelling time of the ridesourcing behavior. We suggest that the traffic behavior of ridesourcing cars indicates specific non-Markovian characteristics, which can be systematically analyzed from the viewpoint of network sciences.