Knowledge Matters™

The other day I was asked “who is the most important person in the network”? Now I don’t like this question because it is laden with all sorts of value judgements. Further there is no right answer because it depends on the subsequent actions and intent. To illustrate my point I will use data from my doctorate, and apply various centrality measures to a ‘problem-solving network’. Consider the map below. It is a directed spring graph produced in NetDraw . The actors in the centre highlighted as yellow nodes appear to be the most important, but are they?

Now consider the map below, which has been produced in NetMiner 3 . (Most of the other visualisations on this website have been produced in NetDraw, but I prefer the ‘target view’ of NetMiner 3 when examining centrality).

Note the two ‘key-players’ in the centre of the target, shown as yellow diamonds. They are the same actors as the yellow actors in the spring diagram. At first blush they still appear to be the most important actors, and confirm the initial analysis. Note also the players coloured as green stars and light blue crosses as well as their relative positions. Now consider the map below.

See how the green-star actors have moved to the centre and the yellow-diamond and blue-cross actors have become peripheral. I’m using the same data, but applying a different algorithm, which I will explain in just a moment. Now consider the map below.

I’m still using the same data, but have applied yet another algorithm. Note this time there is a much more even distribution of actors, and the blue-cross and green-star actors have become central. The yellow-diamond actors are not quite as central, and now some red-circle players are entering the game. So what's going on?

In the first map I applied an in-degree centrality algorithm. This measures the number of incoming ties from one actor to another. The nodes have been sized according to the number of in-links. In the second map I have also used an in-degree algorithm, but the actors with the most incoming ties are placed at the centre of the map. This explains why the second map confirms the diagnosis of the first map. The yellow-diamond actors are hubs, but are they connectors?

In the third map I applied a betweenness centrality algorithm. This measures the extent to which a node lies between all other pairs of nodes on their geodesic paths. To put it another way it measures the ability to access other actors in the shortest distance or number of steps. These actors are the brokers, and have great influence over what flows and does not flow in the network.

In the fourth map I applied community centrality. The larger the centrality value the more influence potential the node has in forming a local community. Nodes with high community centrality play a central role in their local neighbourhood, and are positioned closer to the centre of the map.

So to return to the original question – “who is most important?” The answer is it depends on what you want to know and what you want to do with the information. If you want to weave the network it isn’t the yellow-diamond actors. If you want to measure the effectiveness of a help desk then, assuming the coloured actors are part of the help-desk, the yellow-diamond actors are most important.

I’ve said it before, but it’s worth saying again, you must deeply understand your data, the organisation in question, and the roles of the people in the organisation. The maps are important, but the underlying questions and what you want to do with the maps matters more.

Regards, Graham