MO412 Graph Algorithms Questions

  Imagine a Cayley Tree, constructed starting from a central node of degree k. Each node at distance d from the central node has degree k, until the nodes reachable at distance P that have degree one, as shown in figure above. Consider that there are k+1 communities, where each community corresponds to a leaf of the network and the central node is other community. Considering that the number of nodes reachable in t steps from the central node is computed as k(k-1) t-1 , and  number of links L = N-1, being N the number of nodes, what is the modularity if k=3 and t =4? Round it up to three decimals places. Tip: Try to model the total number of links within the community , L c, and the total degree of the nodes in the community k c as a function of k and t. A. 0.621 B. 0.523 C. 0.785 D. 0.591 E. None of the above. Original idea by: Germán Darío Buitrago Salazar