Agentic systems are modern software systems: they consist of orchestrated modules, expose interfaces, and are deployed in software pipelines. Unlike conventional programs, their execution, i.e., trajectories, is inherently stochastic and adaptive to the problems they solve. Evaluation of such systems is often outcome-centric. This narrow focus overlooks detailed insights, failing to explain how agents reason, plan, act, or change their strategies. Inspired by the structured representation of conventional software systems as graphs, we introduce Graphectory to systematically encode the temporal and semantic relations in such systems. Using Graphectory, we automatically analyze 4000 trajectories of two dominant agentic programming workflows, SWE-agent and OpenHands, with four backbone Large Language Models (LLMs), attempting to resolve SWE-bench issues. Our automated analyses (completed within four minutes) reveal that: (1) agents using richer prompts or stronger LLMs exhibit more complex Graphectory, reflecting deeper exploration, broader context gathering, and more thorough validation; (2) agents' strategies vary with problem difficulty and the underlying LLM - for resolved issues, strategies often follow coherent localization-patching-validation steps, while unresolved ones exhibit chaotic or backtracking behaviors; and (3) even successful agentic systems often display inefficient processes. We also implement a novel technique for real-time construction and analysis of Graphectory and Langutory during agent execution to flag trajectory issues. Upon detecting such issues, the technique notifies the agent with a diagnostic message and, when applicable, rolls back the trajectory. Experiments show that online monitoring and interventions improve resolution rates by 6.9%-23.5% across models for problematic instances, while significantly shortening trajectories with near-zero overhead.