Perhaps the simplest centrality measure is vertex degree: the number of adjacent edges of the vertex. For directed graphs there are three different degree measures: in-degree is the number of edges pointing to the vertex, out-degree is the number of edges pointing from the vertex to other vertices and total degree is the sum of in-degree and out-degree.

To calculate vertex degrees in igraph select the graph and choose one of the degree commands from the “Centrality” menu. For undirected graphs the three commands do the same, they only differ for directed graphs.

You can also calculate the minumum, maximum and mean degree of a graph, for this select the graph and choose “Basic statistics” from the “Statistics” menu. You can select many graphs if you want to compare their properties.

For bigger graphs it is often not only the degree of the individual vertices is important but also its distribution. This means that we count the number of vertices which have degree zero, one, etc. and create a plot from this.

To plot the degree distribution in tkigraph first select “Degree” from the “Centrality” menu and then click on the “Plot distribution” button. You can set logarithmic axis if you want to, this is often useful for graphs having very large degree nodes.

If we are interested in how many steps it requires to get the other vertices from a given vertex then the corresponding centrality measure is called closeness. Closeness measures the average number of steps needed to take to travel to other vertices.

Betweenness measures the extent to which a vertex is “in between” other vertices. The betweenness score of a vertex is the number of shortest paths going through it. For example in an airport network, where two airports are connected if there is a direct flight between them, the betweenness score of the large hubs will be obviously big, as most shortest routes go through them.

TODO