Strength of relationships varies

You already know that not all connections are created equal. You just haven't made that knowledge operational.

Think about the last time someone asked for your opinion on a decision. You probably weighted the opinions of the people around you differently — trusting your closest collaborator's judgment on technical architecture more than a casual acquaintance's, but trusting that acquaintance's read on market trends more than your collaborator's, because the acquaintance works in a different industry and sees patterns your inner circle never encounters.

You were doing relationship-strength analysis. You just weren't doing it explicitly.

Over the first four lessons of Phase 13, you've built up your relationship mapping capabilities in stages. You learned that relationships carry as much meaning as the entities they connect (L-0241). You replaced vague assumptions with explicit connections (L-0242). You classified relationships by type — causal, temporal, hierarchical, associative (L-0243). And you learned that some relationships have direction — that A influencing B is not the same as B influencing A (L-0244).

But there's a critical dimension still missing from your maps: strength. Right now, every edge in your relationship map looks the same. A strong causal link and a tentative association are drawn with the same line, given the same visual weight, treated with the same confidence. That is a model that systematically discards information you already possess. This lesson is about getting that information back.

What "strength" actually means in a relationship

Relationship strength is not a single variable. It's a composite measure that depends on the domain you're mapping and the purpose of your map. But across domains, four dimensions consistently emerge.

Frequency — how often the relationship is active. A colleague you speak with daily has a higher-frequency connection than one you email quarterly. A concept you reference in every project has a stronger link to your working knowledge than one you looked up once three years ago. Frequency alone doesn't determine strength — you can have frequent, shallow interactions — but it's a reliable signal.

Intensity — how much the relationship carries when it is active. A single conversation with a mentor that reshapes your thinking about your career has more intensity than a hundred routine check-ins with a peer. In knowledge systems, a causal relationship where variable A explains 80% of the variance in variable B has more intensity than one that explains 5%. Intensity captures the depth of exchange, the magnitude of influence, the weight of what flows along the connection.

Reciprocity — whether the relationship flows in both directions and at what balance. Strong relationships tend to be reciprocal: both parties invest, both benefit. This applies equally to social connections (mutual trust, shared vulnerability, balanced effort) and to knowledge connections (concepts that inform each other, evidence that supports multiple claims). Highly asymmetric relationships — where all the value flows one direction — tend to be fragile. They persist only as long as the one-directional benefit continues.

Durability — how long the relationship has persisted and how much stress it has survived. A friendship that has weathered a serious conflict and recovered is stronger than one that has never been tested. A hypothesis that has survived multiple attempts at falsification is stronger than one that has simply never been challenged. Duration is not the same as durability — a ten-year relationship that has never been tested may be weaker than a two-year relationship that has been tested repeatedly.

Granovetter, in his original 1973 paper, defined tie strength as "a (probably linear) combination of the amount of time, the emotional intensity, the intimacy (mutual confiding), and the reciprocal services which characterize the tie." Nearly fifty years of subsequent research has refined the measurement techniques, but his core dimensions have held up remarkably well. Strength is not a feeling. It is a measurable composite of observable properties.

The strength of weak ties — and why it matters for your maps

The most consequential finding in the study of relationship strength came from Granovetter's counterintuitive discovery: weak ties are not merely less useful versions of strong ties. They serve a fundamentally different structural function.

Granovetter's 1973 survey of job seekers in the Boston area found that 84% of those who found jobs through personal contacts had done so through someone they saw "occasionally" or "rarely" — not through close friends or family. The reason was structural, not emotional. Your strong ties — your closest friends, your most trusted colleagues — tend to know the same people you know and have access to the same information you have. They are part of your local cluster. Weak ties, by contrast, bridge clusters. They connect you to social worlds you don't otherwise touch. When a weak tie passes you information, it is information you almost certainly could not have obtained from any of your strong ties.

This was validated at unprecedented scale in 2022 when researchers at MIT and LinkedIn published the results of a five-year experiment involving 20 million users. By randomly varying the ratio of weak-to-strong tie recommendations in LinkedIn's "People You May Know" algorithm, they were able to measure the causal effect of tie strength on job mobility. The result confirmed Granovetter's theory with an important refinement: moderately weak ties — connections where two people shared roughly 10 mutual acquaintances — produced the greatest job mobility. Not the weakest possible ties, and not strong ties, but a specific zone of relationship strength that balanced bridge access with enough trust to actually transmit actionable information.

The implication for your relationship maps is direct. If you draw all connections with equal weight, you cannot distinguish the strong ties that provide support and reliability from the weak ties that provide novelty and bridge access. You lose the ability to diagnose your network's actual structure. A map that shows you have "many connections" but cannot tell you which ones bridge to new clusters is a map that looks complete but is functionally blind.

Dunbar's circles: strength as concentric structure

Robin Dunbar, the Oxford anthropologist who proposed the social brain hypothesis, demonstrated that relationship strength doesn't just vary randomly — it organizes into distinct layers with characteristic sizes.

Through studies of phone records, Christmas card lists, Facebook networks, and historical military units, Dunbar and his colleagues found that human social networks consistently organize into concentric circles: roughly 5 people in the innermost support clique (the people you would call in a genuine crisis), 15 in the sympathy group (close friends you see regularly), 50 in the affinity group (friends you would invite to a large gathering), and 150 in the active network (people you maintain a meaningful ongoing relationship with). Each successive layer is approximately three times the size of the previous one, and the strength of ties decreases correspondingly.

This is not arbitrary. It reflects the cognitive and temporal constraints of maintaining relationships. Strong ties require more investment — more time, more emotional energy, more reciprocal attention — so you can maintain fewer of them. Weak ties require less investment per connection, so you can maintain more. The layered structure is not a design choice. It is a consequence of finite human capacity applied to the mathematics of relationship maintenance.

For your cognitive infrastructure, this pattern suggests that your relationship maps should expect and reflect this layered structure. Not every relationship can be high-strength, nor should it be. The goal is not to maximize the strength of all connections but to understand the strength of each one — so you can invest appropriately, route queries correctly, and maintain realistic expectations about what each connection can deliver.

Weighted relationships in knowledge systems

The principle of variable relationship strength extends far beyond social networks. In knowledge systems — personal notes, conceptual frameworks, project architectures — the connections between ideas also vary in strength, and making that variation explicit transforms the quality of your thinking.

Consider how you might map the relationship between sleep deprivation and cognitive performance. You probably believe there is a strong causal relationship. But how strong? And compared to what? Research has established that the relationship between acute sleep deprivation and simple reaction time is very strong — the effect size is large and the evidence is overwhelming. But the relationship between chronic mild sleep restriction and complex creative problem-solving is much weaker and more contested. If your knowledge map draws both connections with the same weight, you'll treat well-established causation and tentative correlation as equally reliable grounds for decision-making.

Researchers studying knowledge graphs — the formal structures used by AI systems to represent relationships between concepts — have developed sophisticated approaches to exactly this problem. Every edge in a well-built knowledge graph carries a confidence score: a numerical weight that represents how much evidence supports the relationship, how reliable the sources are, and how consistent the claim is with other established knowledge. A knowledge graph without confidence scores is just a collection of assertions. With scores, it becomes a model that can distinguish what it knows well from what it merely suspects.

Van Leeuwen's research on belief strength, published in Frontiers in Psychology in 2022, identified two distinct components of how strongly we hold beliefs: epistemic confidence (how close the belief seems to actual knowledge, based on evidence and rational justification) and identity centrality (how important the belief is to who we are). The critical finding is that these two dimensions often diverge. You might hold a belief with low epistemic confidence but high identity centrality — meaning you feel strongly about it despite thin evidence. Or high epistemic confidence but low identity centrality — meaning you're quite certain of it but it doesn't define you. Distinguishing these dimensions in your knowledge maps prevents a common failure: treating emotionally important beliefs as if they were well-evidenced, or dismissing well-evidenced claims because they feel unimportant.

From unweighted to weighted: the practical shift

Moving from unweighted to weighted relationships requires three operational changes in how you build and maintain your maps.

First, define your strength criteria before you start scoring. The biggest mistake is assigning strength intuitively — "this feels like a strong connection" — without specifying what "strong" means. For social relationships, adopt Granovetter's four dimensions (time, intensity, intimacy, reciprocity) or develop your own. For knowledge relationships, consider evidence quality, source reliability, predictive track record, and number of independent confirmations. For project dependencies, consider coupling tightness, failure propagation risk, and substitutability. Write your criteria down. Strength assessment without explicit criteria is just dressed-up guessing.

Second, use a simple scale and resist false precision. A 1-to-5 scale captures the meaningful variation in relationship strength without pretending you can distinguish between a 7.2 and a 7.4. The categories might be: 1 (tentative — minimal evidence or interaction), 2 (weak — some evidence or occasional interaction), 3 (moderate — reasonable evidence or regular interaction), 4 (strong — substantial evidence or deep interaction), 5 (foundational — extensive evidence or relationship you'd stake significant decisions on). Five levels is enough to separate your load-bearing connections from your speculative ones. That is the practical distinction that matters.

Third, schedule strength re-evaluation. Relationship strength is not static. Social ties strengthen and weaken as investment changes. Knowledge links strengthen as evidence accumulates or weaken as contradictory findings emerge. Project dependencies tighten or loosen as architectures evolve. A strength score assigned once and never revisited is an expiration-dated asset. Build periodic re-evaluation into whatever cadence you already use for reviewing your maps — monthly, quarterly, or at natural transition points.

Your Third Brain: how artificial systems learn relationship strength

Neural networks — the computational architecture behind modern AI — are, at their core, systems for learning relationship strength. Every connection between neurons in a neural network carries a numerical weight. That weight determines how much influence one neuron's activation has on the next. When the network trains on data, it is doing precisely one thing: adjusting those weights. Strengthening the connections that lead to correct outputs. Weakening the connections that lead to errors.

This is not a metaphor. It is a direct parallel. The initial state of a neural network is a web of random-strength connections — the computational equivalent of your first draft of any relationship map, where you know connections exist but haven't yet calibrated their importance. Through exposure to data (experience) and feedback (error correction), the network gradually differentiates: some weights become large and positive (strong reinforcing relationships), some become large and negative (strong inhibitory relationships), and many settle near zero (connections that turned out not to matter much). The trained network's knowledge is literally encoded in the strength of its connections.

Weight pruning — a technique where connections near zero strength are removed entirely — demonstrates that most of a trained network's performance depends on a relatively small number of strong connections. Researchers at Stanford showed that neural networks can be pruned to remove 90% of their connections with minimal loss of accuracy. The structural insight is striking: in a trained system, the vast majority of possible connections turn out to be negligible. What matters is the small fraction of high-strength relationships.

The parallel to your personal cognitive infrastructure is precise. You have thousands of potential connections in your professional network, your knowledge base, your project ecosystem. But your actual performance — your ability to make good decisions, find the right information, get things done — depends on a much smaller set of high-strength relationships. Identifying which connections carry the most weight is not a nice-to-have optimization. It is the difference between a system that functions and one that merely exists.

Knowledge graphs used in modern AI systems take this further by assigning explicit confidence scores to every relationship. A fact triple like "sleep deprivation causes impaired reaction time" might carry a confidence score of 0.95 — near certainty, supported by decades of replicated research. A more speculative link like "gut microbiome composition influences creative problem-solving" might carry a 0.3 — interesting hypothesis, early evidence, not yet reliable enough to build decisions on. The knowledge graph doesn't discard the low-confidence relationship. It preserves it while making its weakness explicit. When the system reasons across these relationships, it propagates confidence — a conclusion based on two 0.95 links is treated very differently from one based on two 0.3 links.

You can adopt the same principle. Not every relationship in your maps needs to be strong. Some of your most valuable connections will be weak, speculative, or provisional. The discipline is not in making all relationships strong — it is in knowing which ones are.

Protocol: Strength-audit a relationship map

Here is the operational protocol for adding strength to an existing relationship map. This takes roughly thirty minutes and should be done once per quarter for any map you actively use for decision-making.

1. Select a map. Choose one relationship map — your professional network, a concept map in your notes, a project dependency chart, a personal knowledge graph. If you don't have an explicit map yet, pick a domain and list ten entities and their connections.

2. Define strength criteria. Before scoring anything, write down what "strong" means in this domain. Use 2-4 dimensions. For social: time invested, emotional depth, reciprocity, durability. For knowledge: evidence quality, source count, predictive accuracy, practical impact. For projects: coupling tightness, failure risk, change frequency.

3. Score each relationship. Walk through every connection on your map and assign a 1-5 strength score based on your criteria. Don't agonize — your first honest estimate is usually within one point of where you'd land after careful deliberation. The goal is explicit differentiation, not perfect measurement.

4. Identify the extremes. Find your three strongest relationships and your three weakest. For the strongest: are you leveraging them appropriately? Are you investing enough to maintain their strength? For the weakest: are any of these bridge connections that provide access to information or resources your strong ties cannot? Are any so weak they should be removed from the map entirely?

5. Check for strength assumptions. Find two relationships you assumed were roughly equal in strength. Look at your scores. Are they actually equal? Often you'll discover that a relationship you treated as strong has quietly weakened, or a relationship you dismissed as trivial has become load-bearing without your noticing.

6. Update and date your scores. Record the scores on or alongside your map, with the date. Next quarter, you'll re-score and compare — tracking how relationship strengths shift over time is one of the most revealing patterns in any map.

The output is not a perfect measurement of every relationship's true strength. It is a map that distinguishes the connections you can rely on from the connections you can't — and that is the foundation for every decision, query, and investment you make through your network.

Once you can see that relationships vary in strength, a natural next question emerges: are some relationships not just strong or weak, but structurally ordered? Do some connections have to exist before others can form? That's the territory of prerequisite relationships — and it's where we head in L-0246.

---

Sources

• Granovetter, M. S. (1973). "The Strength of Weak Ties." American Journal of Sociology, 78(6), 1360-1380.
• Rajkumar, K., Saint-Jacques, G., Bojinov, I., Brynjolfsson, E., & Aral, S. (2022). "A causal test of the strength of weak ties." Science, 377(6612), 1304-1310.
• Dunbar, R. I. M. (2021). "Dunbar's number: why my theory that humans can only maintain 150 friendships has withstood 30 years of scrutiny." The Conversation.
• Van Leeuwen, N. (2022). "Two Concepts of Belief Strength: Epistemic Confidence and Identity Centrality." Frontiers in Psychology, 13, 939949.
• Han, S., Pool, J., Tran, J., & Dally, W. J. (2015). "Learning both Weights and Connections for Efficient Neural Networks." Advances in Neural Information Processing Systems, 28.
• Barrat, A., Barthelemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). "The architecture of complex weighted networks." Proceedings of the National Academy of Sciences, 101(11), 3747-3752.
• Shenoy, P. & Yu, S. (2021). "Towards Knowledge Graphs Validation through Weighted Knowledge Sources." arXiv:2104.12622.