D(K, N) ≡ avgx∈N miny∈K |x, y|

We don’t really know about how the k people were chosen to die in these events; for a simple model, we could just assume that they were randomly chosen from the population. Then we can average over all ways to choose k people, and get a notion of the mean separation of people from sorrow in a population:

D(k, N) = avgK⊆N, |K|=k D(K, N)

D(1, N) is simply the mean “Kevin Bacon” distance between two people in a population of size N. D(k, N) is the mean distance between an arbitrary person and an arbitrary group of k people. I think that this is a good measure of the radius of sorrow in any catastrophic event: if you live in a population of N people that are bound in the sort of social network we’re talking about, and k are in some way affected by this, then you are so many degrees away from someone who was hit.

I don’t know if anyone has calculated a function like this for large populations, where the network is basically a country. I suppose it would be straightforward enough to do simulations to compute it.

It seems like a useful thing, though: it would be a kind of language for expressing the impact of a distant catastrophe. Instead of simply being told, “2,500 people died in this earthquake” you could learn something like “the average person was within three degrees of separation of someone who was killed.”

(It occurs to me that the question of which average to use is important: means are probably too sensitive to outliers, and in power-law networks that’s a major issue. A median would be useful, or of course a full histogram) ]]>

D(K, N) ≡ avgx∈N miny∈K |x, y|

We don’t really know about how the k people were chosen to die in these events; for a simple model, we could just assume that they were randomly chosen from the population. Then we can average over all ways to choose k people, and get a notion of the mean separation of people from sorrow in a population:

D(k, N) = avgK⊆N, |K|=k D(K, N)

D(1, N) is simply the mean “Kevin Bacon” distance between two people in a population of size N. D(k, N) is the mean distance between an arbitrary person and an arbitrary group of k people. I think that this is a good measure of the radius of sorrow in any catastrophic event: if you live in a population of N people that are bound in the sort of social network we’re talking about, and k are in some way affected by this, then you are so many degrees away from someone who was hit.

I don’t know if anyone has calculated a function like this for large populations, where the network is basically a country. I suppose it would be straightforward enough to do simulations to compute it.

It seems like a useful thing, though: it would be a kind of language for expressing the impact of a distant catastrophe. Instead of simply being told, “2,500 people died in this earthquake” you could learn something like “the average person was within three degrees of separation of someone who was killed.”

(It occurs to me that the question of which average to use is important: means are probably too sensitive to outliers, and in power-law networks that’s a major issue. A median would be useful, or of course a full histogram) ]]>

Basically, a simplified formula is:

N (Network breadth) = (average number of people each individual knows)

Mean distance in a population = log (base N) of total population

Now, it turns out that in social networks N actually operates under a power law, so an arithmetic mean gives weird results. Some people are just way, way more well-connected than others.

There’s also the fact that people tend to cluster into richly-interconnected clusterss, and that those clusters are usually linked together by folks with very high N values.

But, anyway, it turns out that whatever the value is, the distance is usually quite low, as Kevin Bacon can tell you.

(One of my favorite books talks a lot about social networks – “Linked” by Barabasi. I’m happy to lend if you’re willing to forgive me for redacting my last name out of your very fine poem.) ]]>

Basically, a simplified formula is:

N (Network breadth) = (average number of people each individual knows)

Mean distance in a population = log (base N) of total population

Now, it turns out that in social networks N actually operates under a power law, so an arithmetic mean gives weird results. Some people are just way, way more well-connected than others.

There’s also the fact that people tend to cluster into richly-interconnected clusterss, and that those clusters are usually linked together by folks with very high N values.

But, anyway, it turns out that whatever the value is, the distance is usually quite low, as Kevin Bacon can tell you.

(One of my favorite books talks a lot about social networks – “Linked” by Barabasi. I’m happy to lend if you’re willing to forgive me for redacting my last name out of your very fine poem.) ]]>