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Faculty positions at institutions of higher education are limited resources for which there is a high level of competition. Previous studies have shown that a hierarchy of prestige exists within academia which leads to 80% of those positions being filled by the doctoral graduates from only 20% of institutions. The goal of the current study is to determine whether such a hierarchy also exists within Canadian mechanical engineering programs and to consider other demographic differences within their faculty complements. Information on over 1100 faculty members from the 38 accredited Canadian mechanical engineering programs were gathered from public sources, including their doctoral training institution, their year of graduation, and the name(s) of their faculty advisor(s). It was found that 22% of institutions were responsible for the doctoral training of 78% of faculty members. A PageRank analysis, coupled with k-means clustering, identified four tiers of doctoral prestige and demonstrated that few trainees are hired by a more prestigious institution. For example, only 9% of those trained at a Tier III institution were hired by a Tier II and none by a Tier I institution. Academic advisors also played an important role; 11 unique advisors had five or more of their trainees currently employed in those 38 programs. Only 16.7% of faculty members were female-presenting, lower than the 17.5% proportion of so-called "self-hires" (i.e., those employed by the institution where they did their doctoral training). This study provides analytical tools for quantifying institutional prestige as well as a demographic snapshot of Canadian mechanical engineering faculty that can be used to analyze other fields and jurisdictions. Further research in faculty hiring will benefit students looking to pursue careers in academia, as well as guide those responsible for ensuring equitable hiring practices.