Assortativity of kNN graphs

Research problem definition

Whether there exists a correlation between k parameter of kNN graphs (nodes' number of outgoing connections) and its assortativity coefficient.

Where assortativity is a tendency of nodes to connect to similar nodes.

Why is research of assortativity important?

We can investigate whether real world datasets/networks tend to have nodes more keen to connect to nodes alike them or rather connect to random nodes.

Examples of (dis)assortative networks:

• Social networks - assortative
  • we connect with people that are alike us in terms of age, nationality, income, etc
• Internet - disassortative
  • Internet nodes can connect to any other node

One of received results via implemented solution

Pearson Correlation Coefficient calculation

public double compute() {
  int numLinks = g.getEdgeCount();
  double[] degSrc = new double[numLinks];
  double[] degDst = new double[numLinks];
  
  Collection links = g.getEdges();
  Iterator lit = links.iterator();
  int i = 0;
  while (lit.hasNext()) {
    Link l = lit.next();
    Pair endPoints = g.getEndpoints(l);
    degSrc[i] = g.degree(endPoints.getFirst());
    degDst[i] = g.degree(endPoints.getSecond());
    i++;
  }
  
  PearsonsCorrelation pc = new PearsonsCorrelation();
  return pc.correlation(degSrc, degDst);
}