Keep the network.
Connections and people stay fixed.
Some people have more ways into a sample.
INVESTIGATIONS / NETWORKS & PERCEPTION
Constructed exampleWhy does everyone else seem more connected?
The same people, reached by different paths. Who appears more often?
YOUR TASK / CONSTRUCTED EXAMPLE
Check how the sample finds people
You’re reviewing a fictional network and how people enter a sample. Predict who is most likely to appear, then follow the sampling paths for individual people.
An evidence trail.
Your decision.
Begin with a provisional judgment
Loading the supplied example…
Keep a private first thought (optional)
Private writing stays out of links and default downloads. A reopened link does not restore it.
This records a provisional judgment and the starting configuration. It does not change a mathematical setting or save automatically.
01 / THE QUESTION
Who is most likely to appear in your sample?
The opening star has eight people. One person has seven connections; each of the others has one. What changes when we enter through a connection instead of choosing a person?
Keep a first thought
Optional. Included only when you explicitly save; excluded from shared links.
Constructed data · every relationship and outcome is supplied.
02 / OPEN THE MODEL
—Uniform person meanconnections
—Uniform edge-end meanconnections
—Undirected connectionsedges
The way you sample changes the world you see.
Choosing a person uniformly gives everyone equal weight. Choosing an edge uniformly, then one of its ends uniformly, weights each person by their number of connections.
Save this experiment
Explore the model and compare working versions
Follow the idea.
A concept, in three framesChange the entry point.
A person and an edge-end are different samples.
Compare the weights.
More connections create more ways to be reached.
HOLD ONE VERSION STILL
What changes when you change the model?
Keep the current inputs beside your next adjustment.
MODEL & LIMITS
What this model leaves open
These are two exact sampling procedures on a supplied graph. They do not show that every person has fewer connections than their contacts, or measure friendship quality.
- InputsWhat is supplied?
- DefinitionWhat is counted?
- InferenceWhat follows?
Inspect the exact workings
Sum of degrees = 14 = 2 × 7 edges. Sum of squared degrees = 56. Person mean = 14/8 = 1.75. Endpoint mean = 56/14 = 4.
| Person | Neighbors | Degree | Person weight | Edge-end weight |
|---|---|---|---|---|
| A | B, C, D, E, F, G, H | 7 | 1/8 | 7/14 |
| B | A | 1 | 1/8 | 1/14 |
| C | A | 1 | 1/8 | 1/14 |
| D | A | 1 | 1/8 | 1/14 |
| E | A | 1 | 1/8 | 1/14 |
| F | A | 1 | 1/8 | 1/14 |
| G | A | 1 | 1/8 | 1/14 |
| H | A | 1 | 1/8 | 1/14 |
Connections: A—B, A—C, A—D, A—E, A—F, A—G, A—H. For a nonempty edge set, the two means differ by degree variance divided by mean degree. Equality holds when every person has the same degree.
Assumptions, sources and evidence status
Original constructed fixture: constructed-networks-v1. networks-v1. No empirical observations are represented by these example counts.
- Uniform edge-end sampling is not uniform-person-then-neighbor sampling.
- An edgeless graph has no endpoint sampling distribution; its endpoint mean is undefined.
- Degree is not worth, friendship quality or proof that every person has fewer connections than their contacts.