Neither is prior; the distinction is a modeling choice, not a fact about the world.
The case for objects first. In standard set theory, relations are defined as sets of ordered pairs, and ordered pairs are themselves built from sets of objects: $(a,b) = {{a}, {a,b}}$ (Kuratowski).
On this foundation, edges are literally constructed from nodes and cannot exist without them. Most mathematics and most programming inherit this asymmetry: a graph is formally a pair $(V, E)$ where $E \subseteq V \times V$, so vertices are logically prior.
The case for relationships first. Category theory reverses the emphasis: objects are often opaque points whose entire content is exhausted by the morphisms into and out of them.
The Yoneda lemma makes this precise — an object is determined up to isomorphism by its pattern of relationships to all other objects.
In this frame, "what a thing is" is its edges; the node is a placeholder. In physics, structural realism argues the same: our epistemic access is to relations (symmetries, correlations), not to intrinsic natures of relata (this is a contested interpretive position, not settled).
Why the question has no forced answer. The two are interdefinable. Given objects and a rule, you generate relations; given a relation, its field (the objects it connects) is recoverable as a projection.
You cannot bootstrap one from literally nothing — an edge with no endpoints and a node with no possible connections are both degenerate. The apparent priority always comes from a chosen foundation, and foundations are conventions selected for convenience, not discovered.
Practical upshot. Choose objects-first when entities have stable identity independent of context (database records, physical particles with intrinsic properties). Choose relations-first when identity is defined by role (kinship terms, morphisms, offices, tokens in a protocol) — modeling these as pre-existing objects introduces spurious identity.
This verdict reverses if someone exhibits a coherent formalism in which one is derivable without any implicit appeal to the other — a genuine asymmetric reduction rather than a mutual interdefinition. No current foundation does this; each smuggles in the counterpart as a primitive.
Relationship is first—the edge precedes the node.
Here's the reasoning: a node with no edges is undetectable. It has no properties you could observe, because every property is really a relationship in disguise—mass is a relation to a gravitational field, position is a relation to a frame, "red" is a relation between a surface and an observer. Strip away all relations and nothing remains to point at. So what we call an "object" is a relatively stable bundle of relationships that we've reified into a thing for convenience.
This isn't just wordplay; it shows up concretely:
The intuitive answer feels like "object first" because our perception hands us pre-packaged things and hides the relational scaffolding that produced them. That's a feature of cognition, not of reality.
The honest caveat: it depends on what you mean by "first." If you mean ontologically prior—what can exist without the other—relationship wins, since nodes are derivative. If you mean epistemically first—what we notice and name earliest—objects win, because relations are inferred from the stable things they connect. Both are true at different layers, but the deeper answer is that the distinction dissolves: there are no bare nodes and no floating edges, only a web where the knots and the threads define each other simultaneously.
Start with physics at its most austere. Reach into quantum field theory and you find no objects at all — only fields, and the fields are nothing but ways of relating excitations across spacetime. A particle is a standing wave of interaction, a knot momentarily tied in a rope of relationship. The electron does not have charge as a possession the way you have a coat; charge is the way it couples to the electromagnetic field. Strip away every relationship an electron participates in and you have removed the electron itself. There is nothing left over. The edge, in this reading, is not stretched between pre-existing nodes — the nodes condense out of a dense weather of edges, like droplets from saturated air. The relata are precipitations of the relation.
And yet — press the opposite thumb. An edge is defined by what it connects. "Between" presupposes two somethings to be between. A relationship with no relata is not a relationship; it is a grammatical ghost. You cannot love without a beloved, cannot measure distance without two points, cannot even state an edge — A—B — without the letters. Every attempt to make relation primary smuggles objects back in through the vocabulary. This is Aristotle's revenge: relation is the thinnest of his categories, an accident that must inhere in substances. The map needs pins before it can draw string between them. From this angle the question answers itself by tautology — an edge is literally made of its endpoints, so how could it precede them?
Notice that both threads above cheat by assuming time — "first," "precede," "condense out of." But the object–relation pair may not be sequential at all. Consider Buddhist pratītyasamutpāda, dependent origination: nothing arises independently, everything co-arises. There is no first mover in the chain because the chain is a loop. The self and the world, the perceiver and perceived, inter-are. This isn't mysticism dodging the question — it's structural. In a truly relational ontology, "which came first" is a malformed query, like asking which side of a coin was minted first, or whether the peak or the valley of a wave has priority. They are two readings of one gesture. The dichotomy is an artifact of a grammar that forces us to name a subject before a predicate.
Watch a child, or a machine, learn. Word embeddings — the guts of modern language models — encode this beautifully: a word means nothing in itself. "King" is a point in space defined entirely by its distances to "queen," "throne," "man," "power." The object (the token) is a bare index; all its content lives in the edges. This is Saussure a century early — dans la langue il n'y a que des différences — in language there are only differences, with no positive terms. The sign is pure relation; the signifier is arbitrary. Here relationship is emphatically, operationally first: identity is downstream of difference. You are who you are because of everyone you are not. The node is an intersection of edges given a name for convenience, the way a city is really just a thickening of roads.
Perhaps the deepest move is to notice the question is frame-relative, and different disciplines have opposite gravity. Set theory builds relations from objects — a relation is a set of ordered pairs, and sets of what? Of elements. Objects to the bone. But category theory, its rival foundation, inverts this: it forgets what objects are and cares only about the arrows (morphisms) between them. An object in a category is knowable only through its relationships — two objects with identical patterns of arrows are, categorically, the same object. Same mathematics, opposite metaphysical polarity. So the honest answer is that "object-first" and "relation-first" are not truths about the world but choices of coordinate system, and — the surprising part — they turn out to be dual descriptions of the same structure, translatable into each other, like position and momentum, like particle and wave. The question is real; the forced choice between the two answers is the illusion. What is first is the tension that makes both askable.
Neither object nor relationship holds absolute priority; the apparent precedence is an artifact of which framework one adopts rather than a fact about the world. The two are interdefinable—set-theoretic foundations build relations from objects while category theory determines objects entirely through their relations—and each formalism covertly presupposes the counterpart it claims to derive, so no genuine one-sided reduction exists. A node with no edges and an edge with no endpoints are both degenerate: identity and relation define each other simultaneously. What differs is only the useful choice, made per case according to whether entities have stable intrinsic identity or are constituted by their roles.