The advancement of large language models (LLMs) struggles with the scarcity of high-quality, diverse training data. To address this limitation, we propose LinkSyn, a KP-graph-based synthesis framework that for the first time enables flexible control over discipline and difficulty distributions while balancing KP coverage and popularity. LinkSyn extracts KPs from question-answering (QA) seed data and constructs a KP graph to synthesize diverse QA data from multiple seeds strongly linked by KPs and sampled from graph walks. Specifically, LinkSyn incorporates (1) a knowledge value function to guide the adjustment of path sampling probability and balance KP coverage and popularity during graph walks; (2) diffusion-based synthesis via a strong reasoning model by leveraging multiple seeds with dense logical associations along each path; and (3) high-difficulty QA enhancement within given disciplines by flexible difficulty adjustments. By executing LinkSyn, we synthesize LinkQA, a diverse multi-disciplinary QA dataset with 50B tokens. Extensive experiments on Llama-3 8B demonstrate that continual pre-training with LinkQA yields an average improvement of 11.51% on MMLU and CMMLU, establishing new SOTA results. LinkQA consistently enhances performance across model size and initial FLOPs scales.