MCSN Thursday, 15-Sep-11

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Today's assignment

Read sections 1.3.3 to 1.5; submit 1.6; come to class prepared with a Pajek example drawn from the Web, and illustrating chapter content. This will be a regular Thursday assignment. This week, the ESNAP readings focussed on a directed graph, so any directed graph from the web is fine. For instance, you could extract a portion of Twitter.com "following" relations, or look at musician relations (influences, influenced by) on allmusic.com. The point is to create a directed graph in Pajek.

Question of the day

  • Definition: Combinatorics: counting the number of structures with particular properties. (e.g. the number of different connected, undirected, simple graphs on 4 vertices)
  • Definition: "Different": non-isomorphic
    • Here, "different" means "non-isomorphic".
    • Isomorphic graphs contain the same connection information
    • E.g.: a square and a trapazoid and a twisted square graph are all isomorphic
    • Energizing graphs in Pajek always generates an isomorphic equivalent


  • Question: What is the relevance of graph combinatorics to the cross-cultural study of musical groups? What might be revealed by an investigate of the relation between non-isomorphic graph types, and the dynamics of performance?

Brainstorming continues...

Homework exercises from Tuesday - review

Nuts-and-bolts: how to create networks in Pajek

  • Creating and manipulating networks in Pajek itself
  • Editing Pajek files in a text processor
    • Edge and arc list formats
    • Matrix format
  • Using txt2pajek
  • Using a programming language (e.g. scripting language such as php, perl, etc.) to generate Pajek files
  • More combinatorics...
    • How many lines does a complete simple graph on n vertices contain?
      • Undirected graphs
      • Directed graphs
    • How many different undirected simple graphs are there on n vertices?