3. Lesson 3. Calculating various properties of graphs.

In our next example we will calculate various centrality measures in a friendship graph. The friendship graph is from the famous Zachary karate club study. (Web search on 'Zachary karate' if you want to know more about this.) Centrality measures quantify how central is the position of individual vertices in the graph.

```#include <igraph.h>

int main(void) {
igraph_t graph;
igraph_vector_t v;
igraph_vector_t result;
igraph_real_t edges[] = { 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8,
0,10, 0,11, 0,12, 0,13, 0,17, 0,19, 0,21, 0,31,
1, 2, 1, 3, 1, 7, 1,13, 1,17, 1,19, 1,21, 1,30,
2, 3, 2, 7, 2,27, 2,28, 2,32, 2, 9, 2, 8, 2,13,
3, 7, 3,12, 3,13, 4, 6, 4,10, 5, 6, 5,10, 5,16,
6,16, 8,30, 8,32, 8,33, 9,33,13,33,14,32,14,33,
15,32,15,33,18,32,18,33,19,33,20,32,20,33,
22,32,22,33,23,25,23,27,23,32,23,33,23,29,
24,25,24,27,24,31,25,31,26,29,26,33,27,33,
28,31,28,33,29,32,29,33,30,32,30,33,31,32,31,33,
32,33
};

igraph_vector_view(&v, edges, sizeof(edges)/sizeof(double));
igraph_create(&graph, &v, 0, IGRAPH_UNDIRECTED);

igraph_vector_init(&result, 0);

igraph_degree(&graph, &result, igraph_vss_all(), IGRAPH_ALL,
IGRAPH_LOOPS);
printf("Maximum degree is      %10i, vertex %2i.\n",
(int)igraph_vector_max(&result), (int)igraph_vector_which_max(&result));

igraph_closeness(&graph, &result, igraph_vss_all(), IGRAPH_ALL);
printf("Maximum closeness is   %10f, vertex %2i.\n",
(double)igraph_vector_max(&result), (int)igraph_vector_which_max(&result));

igraph_betweenness(&graph, &result, igraph_vss_all(),
IGRAPH_UNDIRECTED);
printf("Maximum betweenness is %10f, vertex %2i.\n",
(double)igraph_vector_max(&result), (int)igraph_vector_which_max(&result));

igraph_vector_destroy(&result);
igraph_destroy(&graph);

return 0;
}
```

This example reflects some new features. First of all, it shows a way to define a graph simply as defining a C array with its edges. Function `igraph_vector_view()` creates a view of a C array. It does not copy any data, this also means that you should not call `igraph_vector_destroy()` on a vector created this way. This vector is then used to create the undirected graph.

Then the degree, closeness and betweenness centrality of the vertices is calculated and the highest values are printed. Note that the vector (`result`) which returns the result from these functions has to be initialized first, and also that the functions resize it to be able to hold the result.

The `igraph_vss_all()` argument tells the functions to calculate the property for every vertex in the graph, it is shorthand for a vertex selector (igraph_vs_t). Vertex selectors help performing operations on a subset of vertices, you can read more about them in one of the following chapters.