Follow the idea.
A concept, in three framesKeep the network.
Connections and people stay fixed.
Change the entry point.
A person and an edge-end are different samples.
Compare the weights.
More connections create more ways to be reached.
A WORKING DEFINITION
Network sampling
A sampling procedure determines how often each member can enter a sample. In a simple undirected network, a person’s degree is their number of connections. Uniform edge-end sampling reaches a person in proportion to that degree.
FOLLOW ONE EXAMPLE
The way you sample changes the world you see.
In the eight-person star, the degrees sum to14, so the uniform-person mean is14/8=1.75. Squared degrees sum to56, so the uniform-edge-end mean is56/14=4. The center has weight1/8 as a person and7/14 as an endpoint. With no edges, endpoint sampling is undefined. Choosing a person first and then their neighbor is a different procedure.
Work through the investigation →WHERE THE CLAIM STOPS
Keep the assumptions attached.
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.
Inspect this model’s assumptions and definitions
- 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.
Definitions used in this instrument
- graph
- simple-undirected-1-to-20-nodes-max-60-edges
- person
- uniform-person-mean-sum-degree-over-node-count
- endpoint
- uniform-edge-then-uniform-end-mean-sum-squared-degree-over-sum-degree
- positions
- view-only-no-weight
SOURCES & SCOPE
Read beyond the model.
Feld (1991), Why Your Friends Have More Friends Than You Do ↗
Primary analysis of degree-weighted friendship distributions and individual comparisons. This page uses an original star and ring, not the paper’s empirical friendship data.
All example data, figures and exact calculations on this page are original constructed teaching material. Source publications provide conceptual background, not the example dataset.
Open the instrument →