This topic introduces the mathematical and computational representations that transform relational data into algebraic structures suitable for large-scale analysis. The adjacency and incidence matrices are presented as the fundamental formats through which networks become computable objects, enabling algebraic operations such as matrix multiplication, eigenvector decomposition, and path enumeration. The conceptual shift from graph traversal to linear algebra is described as a key innovation that allows modern computational social network analysis (CSNA) to exploit the efficiency of optimized matrix operations.

The handout further explores weighted and labeled networks, illustrating how attributes and tie strengths enrich topological interpretation and extend the analytical vocabulary of centrality, redundancy, and homophily. Finally, issues of computational efficiency are examined, comparing dense and sparse representations and introducing scalable data structures such as adjacency lists and compressed sparse row formats. The topic concludes that representation is both an intellectual and engineering choice that determines what aspects of a network can be meaningfully computed.

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