Applied Mathematician for Geospatial Data Architecture — Graph Theory & Discrete Mathematics

We are developing a Canadian geospatial intelligence system that will organize millions of geographic, economic, real estate, infrastructure, and institutional records. The system will use approximately 900,000 Canadian postal codes as a geographic indexing layer, connecting them with: 10+ million property addresses Municipalities, provinces, and territories Businesses and government organizations Schools, universities, and healthcare facilities Infrastructure assets and projects Indigenous communities Census, economic, and real estate data The long-term objective is to enter any Canadian postal code and generate a structured profile of the surrounding area, including nearby institutions, infrastructure, businesses, demographic characteristics, economic indicators, and real estate information. We are seeking an applied mathematician to help design the system from first principles using discrete mathematics, graph theory, set theory, relational structures, and practical data-modeling concepts. This is initially an architecture and research assignment—not a large software-development contract. Core Questions The selected mathematician will evaluate: Whether the system should be represented primarily as a graph, hierarchy, relational model, interconnected graphs, or hybrid architecture. The major mathematical sets and entities within the system. Appropriate node types, edge types, directions, weights, and relationship rules. How geographic hierarchies and overlapping boundaries should be represented. How permanent identifiers should be assigned to millions of objects. Which mathematical concepts and algorithms will be most useful as the system develops. How new datasets can be added without redesigning the underlying architecture. How the theoretical model should translate into practical database implementation. Potentially relevant concepts include: Graph traversal Clustering and community detection Connected components Centrality Nearest-neighbour analysis Shortest paths Spatial relationships Bipartite and multilayer graphs Set membership Matching and optimization Hierarchical and overlapping classifications Temporal graphs and changing relationships Initial Deliverable Please provide a concise architecture report containing: Recommended mathematical architecture Identification of major sets and entity types Proposed node and edge structure Recommended geographic hierarchy Identifier strategy Relevant algorithms and mathematical concepts A conceptual entity-relationship or graph diagram Practical implementation recommendations Recommended first proof of concept Important assumptions, risks, and common modeling mistakes The report should explain the recommendations in plain English while referencing graph theory and discrete mathematics where appropriate. A strong initial engagement may lead to additional paid work designing individual models, reviewing implementations, and supporting the system’s development. Ideal Background We are particularly interested in candidates with experience in one or more of the following: Applied mathematics Discrete mathematics Graph theory Network science Operations research Mathematical modeling Computational geometry Geographic or spatial networks Knowledge graphs Relational database modeling Python, NetworkX, SQL, or PostgreSQL/PostGIS A mathematics student, graduate student, researcher, or experienced independent mathematician may be suitable. Formal GIS experience is helpful but not mandatory. The ability to translate mathematical ideas into a scalable and understandable system is more important than knowing a particular software platform. Application Questions Please answer the following: How would you initially represent a system connecting properties, postal codes, municipalities, institutions, infrastructure, and businesses? Would you recommend a relational database, graph database, or hybrid architecture? Why? Describe one real-world network or data architecture you have previously modeled. Have you implemented graph algorithms in Python, NetworkX, SQL, or another programming environment? How would you distinguish genuine geographic hierarchy from overlapping geographic relationships? What would you include in the first proof of concept? Please provide an example of previous mathematical modeling, graph theory, or data-architecture work. Please begin your application with the words “Geospatial Graph” so we know you have read the complete posting. Project Structure Initial 3 Five Hour Consultants to Determine Appropriate Approach Expected timeline: approximately 1–2 weeks Potential for continuing project-based work Clear written communication required All work must be original and practically applicable