NOTE – at times this post reads like a mechanical, and very contrived, prescription for deciding whether to follow someone on Twitter according to how ‘useful’ they may to you. I know friending/following is a lot more fluid/ad hoc than this, but that’s not the point, okay…? (though I’m not sure what the actual point is, yet…?!)

Part of the rationale for this is so that I can start reading about formal social network analysis with some sort of prior knowledge about what sorts of measures I think might be useful, and why, along with how easy they are to calculate in practice. And along with that, I was also looking for easy to do calculations that might be useful in the context of friend recommendation algorithm. (It also occurs to me that this sort of thinking might be tangentially useful to the development of ‘trust’ or ‘reputation’ metrics that Martin is so keen on… e.g. Some more thoughts on metrics ;-)

So here’s where I got to, comparing myself and @jamesclay in the context of a sample of altc2009 hashtagger:

The first metric is easy enough to calculate – @jamesclay’s friends/followers ratio. When rating how valuable a node might be in a network, I think the ratio of input (“friends”) edges to output (“followers”) edges is a useful one. If the number if close to zero, the node is acting in a largely broadcast mode. My friends/followers ratio is about 0.2-0.25 – approx 4 followers per friend, which works for me. Looking at the magnitude of the number of followers also gives you a clue as to how well connected a node is as a potential amplification channel.

The next pair of numbers I calculated related to the number of mutual friends and the number of mutual followers between myself and @jamesclay, normalised against my total number of friends and my total number of followers respectively.

The first measure – my “normalised mutual friends” tells me what proportion of my friends are also jamesclay’s friends. That is, what proportion of my friends are mutually ‘trusted’ by the person I’m considering following (where friending someone on twitter is taken as a vote of trust; we might also take the number of friends to be the number of people who can influence us on Twitter?). As this number tends to 1, it tells me the extent to which all the people I follow are also followed by @jamesclay. If this number equals one, @jamesclay has friended all the people I have. Although note that in that case, this may only be a small proportion of @jamesclay’s total friends list. (So maybe I need a measure to accommodate that? Eg the number of mutual friends normalised against @jamesclay’s total number of friends?) If the number tends to zero, then very few of my influenced

My “normalised mutual followers” score tells me what proportion of my followers are also jamesclay’s followers. That is, what proportion of my followers mutually ‘trusted’ both myself and jamesclay. If this number tends to one, all my followers are also following jamesclay; which would mean that a tweet from jamesclay would reach all my followers and maybe more. If the number tends to zero, we potentially influence completely different sets of people.

(I guess there’s a number we can grab here which is our shared audience size, that is, the number of our combined unique followers: my_followers+your_followers-mutual_followers. Dividing this by my_followers then gives an amplification factor if ‘you’ retweet me?)

The next two measures are based on the number of my friends who follow jamesclay. That is, the people I trust (as demonstrated by my friending them) who in turn trust (have friended/are following) jamesclay.

The first number is the number of my friends who follow jamesclay, divided by the total number of his followers. That is, what proportion of jamesclay’s followers are my friends? Or to put it another way, what proportion of jamesclay’s total following do I trust?

The last number is the number of my friends who follow jamesclay divided by the total number of my friends. That is, what proportion of my friends trust jamesclay.

Okay, so I have no idea where any of this is going, but I just needed to write it down so that I don’t have to remember it, but know that I can call on it if i do need it…;-) I fully expect that things relating to all the above have been properly worked out in the context of ‘proper’ social network analysis, but I’m still trying to generate my own context to make reading that stuff relevant.

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