Paths in network, degree of vertices

1. Definitions of paths in graph
   • walk, chain and path
   • closed walk, cycle, closed chain, loop
   • length and value of path
   • the shortest path, diameter
   • k-neighbor
   • depth of vertex in acyclic graph
2. Degree of vertex
   • input degree
   • output degree
   • all degree
3. Paths and degrees in Pajek

1. Find degrees, shortest paths, paths with the lowest value and distances from selected vertex.
2. Find depths in acyclic networks.

1. Find diameter, draw the longest shortest path. Find out if there are loops in the network and if the network is acyclic (in this case find depths of vertices). Determine input, output and all degrees of vertices. Find distances from the vertex with the highest output degree. Find the shortest path between vertices with the lowest all degrees (if it exists).

2. Explanation and interpretation of results.

1. Doreian, P., Batagelj, V. in Ferligoj, A. (1999): Clustering Networks: A Generalized Blockmodeling Approach (not published yet), chapter 3.4.