Network centrality and shared skills

(These posts are mostly about my personal learning and how I am developing my skills. You can see my Skill Profile here. I also write on skills and talent and on market segmentation, customer targeting and pricing.)

Continuing my exploration of graph theory and its applications, one of my main learning themes this year, I am exploring the concept of network centrality and its applications to my own work. Centrality is a key concept of graph theory. Looking at a graph (a collection of edges and nodes, with the edges connecting the nodes) one often wants to know the role of the different nodes. One way to answer this is the by looking at a node's centrality.

There are a number of different ways of measuring a node's centrality. Let's look at Degree Centrality, Closeness Centrality, Betweenness Centrality and Eigenvector Centrality.

(If you want to go deeper into this and look at the math behind these concepts, this page is a good place to start. Wikipedia also has a good article on Centrality.)

Degree Centrality - is determined by the number of connections

Closeness Centrality - finds the nodes that are closest (as measured by the number of edges one needs to travel across) to the other nodes (or some subset of nodes)

Betweenness Centrality - identifies the nodes that are on the paths between nodes

Eigenvector Centrality - is a measure of the influence of a node in a network

For eigenvector centrality, relative scores are assigned to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes. Google PageRank is one application of this.

These different measures of centrality can give very results. Alberto Manuel's End to End BPM gives a good example of this.

To see just how different these four measures are look at the following image.

The same network shown four times. Color coding indicates centrality for different measures. Red nodes are more central and blue nodes are less central. Version (a) is degree centrality, (b) uses closeness centrality, (c) shows betweenness centrality, and (d) is eigenvector centrality. Note how clustered the Eigenvector nodes are. Nodes with high degree centrality are more scattered. The closeness measure alco finds a group of nodes that are all, well, close to each other but a different set than the Eigenvector cluster. The nodes high in betweenness are on the paths between clusters.

This visualization is adapted from Claudio Rocchini. Take some time to explore the wonderful images, music and generative art on his site.

How can this be applied to Ibbaka's work?

This is something we have begun to explore with the Ibbaka Skill Graph. (Read what Gregory Ronczewski has to say about the Skill Graph.)

One of the key concepts at Ibbaka is that of connecting skills. These come in two flavors, Internal Connecting Skills and External Connecting Skills. We first noticed these skills when David Botta was doing research on skill clustering. When asked to do a card sorting exercise, and arrange their skills into clusters there were often a few stray skill cards placed between groups. When David asked about this, people explained that these were the skills they used to connect different skill sets. He named these 'connecting skills' and they are proving to be a key to how we understand human potential. Internal connecting skills can suggest paths to building new skills.

It did not take us long to realize that connecting skills also exist between people. When examining a team's skill one generally finds a small group of skills shared by several members. These are part of the connective tissue that helps the team to work together effectively. We refer to these a External Connecting Skills and we try to build them as we develop our own teams.

In graph theory terms, it seems likely that the connecting skills are those that score high on betweenness centrality. If this is true, we are still investigating this, we now have a powerful mathematical tool to discover connected skills.

This leads to the obvious question, do degree centrality, closeness centrality and Eigenvector centrality also have special significance in the Skill Graph?

Answering this is going to require some initial filtering. As there are several types of edges in the Skill Graph, it will be simpler to look at centrality for one type of edge at a time, and then to compare the results for different types of edges. Beginning with skill-to-skill edges, I am speculating about the following.

Degree Centrality will find parent skills.

Closeness Centrality may find associated and complementary skills

Eigenvector Centrality will find tightly clustered groups of the most important skills.

Associated skills are skills that are frequently found together in the same person. For a geeky example, RDF and OWL are associated skills for semantic engineers.

Complementary skills are skills frequently found together on the same team, but are generally held by different people. In a restaurant, the pastry chef and grill chef are both important, but they are almost never the same person.

If I am right that closeness centrality finds complementary and associated skills, it will be easy to distinguish complementary from associated skills by adding back in the edges connecting skills to people and people to people.

To explore this I plan to download a portion of of the Skill Graph to Neo4j for exploration. Neo4j is a graph database platform. It is a great way to explore the properties of connected data sets.

Aside: One can also apply notions of centrality to edges. I like this way of thinking as it shifts attention from the nodes to the connections between the nodes. I have not experimented with this yet, but there is some interesting research going on around this. See for example "Quantifying edge significance on maintaining global connectivity" by Yuhua Qian et al. There is something about shifting attention from nodes to edges that reminds or of IDEF0, where it is the verbs that go in the boxes instead of the nouns.

One of the origins of Ibbaka is a project Lee Iverson and I led early this century on an IDEF0 model of knowledge management.