Meaning matters in the way people form social ties. Adopting an unconventional analytic technique--the Galois lattice analysis--I show how network researchers can uncover relational meanings using conventional research techniques (i.e., closed-ended network surveys). Galois lattice analysis also inspires new ways of conceptualizing relational meanings in terms of the duality of persons and relationships, that is, how actors' understandings of each other as persons define the understandings of their relationships with them, and vice versa. The co-constitution of these dualistic meanings thus defines a "network culture." Comparing two communal settings in which the meaning of "love" is constructed, I demonstrate that different network cultures produce different meaning structures that guide how actors relate to one another, resulting in different degrees of group stability. (Includes 1 table, 6 figures, and 30 endnotes.)