This thesis presents localized methods for traffic prediction and analysis. The prediction method presents an extension of a state-of-the-art Graph Neural Network inspired by traffic flow characteristics on a local level. This inspiration from traffic flow characteristics consists of two parts. The first intuition is that state at some location and at time T in the future will be not influenced by information which is further than traveling time T away. The second intuition is that traffic information traveling with or against the stream of traffic behaves differently. The developed model leverages these intuitions to increase model prediction performance. Further, a modification is made which allows the model to be applied at an arbitrary location in a network, at the cost of performance. Alongside these model extensions, a novel method of visualizing a local traffic state is presented through constructing a novel traveltime diagram. This diagram can be used as a visual tool for analyzing traffic locally. Further, the traveltime diagram is designed to be summarized using Topological Data Analysis to a quantity called the Travel Lifetime which can represent traffic states ranging from extremely calm to imminent congestion to a congested state in a single number. The newly proposed Travel Lifetime is tested as an input to a Neural Network model for predicting traffic speed showing that its use as an input can improve model performance.