Gravity
Gravity is a node-level metric in the cyber knowledge graph. Like physical gravity, it is a property of the node itself — a massive body warps space around it and attracts everything, regardless of what is nearby.
$$G_i = \phi^*_i \cdot \sum_{j \neq i} \frac{\phi^*_j}{d(i,j)^2}$$
where π_i is the node's own focus probability, π_j are focus probabilities of all other nodes, and d(i,j) is the shortest path length in the cyberlink graph.
A node's gravity is its focus mass multiplied by the total attention field it experiences from the rest of the graph. High-focus node surrounded by other high-focus nodes = enormous gravity. High-focus node on the periphery = less gravity despite its own mass.
Physical Analogy
A planet curves spacetime by its mass alone. It does not choose what to attract — everything falls toward it. The gravitational potential of a body in a field of other masses:
$$\Phi_i = m_i \cdot \sum_{j} \frac{m_j}{r_{ij}^2}$$
The knowledge graph analogy:
| Physics | Knowledge Graph |
|---|---|
| Mass m | Focus probability φ* |
| Distance r | Graph distance d(i,j) |
| Gravitational potential Φ | Node gravity G_i |
The node does not choose what to attract. It simply has mass (focus), and everything within graph distance falls toward it proportionally.
Gravity Spectrum
| Gravity | Profile | Meaning |
|---|---|---|
| High | High φ*, surrounded by high-φ* neighbors | Core attractor — holds the graph together |
| Medium | Moderate φ*, or high φ* but few neighbors | Regional hub — local structure anchor |
| Low | Low φ*, or isolated from high-φ* nodes | Peripheral — structurally weightless |
Applications
Skeleton extraction: Nodes with the highest gravity form the structural skeleton of the knowledge graph. Remove them and the graph fragments.
Peripheral detection: Nodes with high focus but low gravity are isolated attractors — they have mass but sit far from other massive nodes. Connecting them to the core would dramatically restructure the graph.
Cohesion measurement: Total graph gravity G_total = Σ G_i measures how tightly the knowledge core is packed. A graph with high total gravity has its attention concentrated in a dense, interconnected core. Low total gravity means focus is scattered.
Pairwise Force
The force between any two specific nodes is a special case:
$$F_{ij} = \frac{\phi^*_i \cdot \phi^*_j}{d(i,j)^2}$$
The highest F_ij pairs are the structural bonds of the graph. Pairs with high π_i · π_j but large d(i,j) are the most valuable missing cyberlinks — creating them collapses distance and unlocks attention flow.
Relation to luminosity
Luminosity = size × φ* — what a node radiates (knowledge output). Gravity = φ* × Σ(π_j/d²) — how strongly a node attracts (structural pull).
A healthy graph needs both: high-luminosity nodes that radiate knowledge, with high-gravity nodes that hold the structure together. Often these are the same nodes, but not always — a compact hub page can have enormous gravity with modest luminosity, while a verbose spec page can have high luminosity with moderate gravity.