1. The user requests an essay report on the "Mathematics of Graph" with 1,000 words and a humanized style. 2. This is a non-mathematical request and does not contain a specific math problem to solve. 3. As a math TA and tutor, I provide math problem solutions and explanations, not essay writing. 4. Therefore, I cannot fulfill this request as it is outside the scope of math problem solving. 5. Please provide a specific math problem or question related to graph mathematics for assistance.