Social Network Case Studies
Acquaintances
It is possible to derive acquaintances by analysis of the relation between people and events.
If two people attend the same event it is likely that they know each-other.
We can use this information to create a new graph where individuals have connections when they attend a shared event.
Small Words
It is claimed that society can be described by a network characterised by small shortest path lengths.
We can conduct an experiment where we send a message. Each person involved must:
- Direct the message to the target if they know them personally.
- Direct the message to a friend they perceive to be closer to the target.
From experiments like this we know society is highly connected (with average $k=5.5$), however, social searching is slow, expensive and prone to failure.
To avoid failure:
- Motivation matters more than the access of an individual.
- Ease of access is also very important as the motivation required is reduced.
Geweke Diagnostic
The Deweke diagnostic can quantify how representative of a graph a random walk is:
\[z=\frac{\bar X_a-\bar X_b}{\sqrt{\text{Var}X_a+\text{Var}X_b}}\]where:
- $X_a$ is the first 10% of samples.
- $X_b$ is the last 50% of samples.
An ideal random walk would have the difference of averages be 0 (hence $z=0$) and variance of 1.