acset

data frame

• a collection of 1-dimensional arrays, called columns, all of the same length
• a row in a data frame consists of the values of all columns at a given integer index
• retrieval
  • individual columns can be retrived by name
  • individual rows can be retrived by index
• storage: dataframe are stored column-wise

graph

• two way to implement its data structures:
• 1. edge list, g
  • data
    • vertices :: int
      • vertices are consecutive numers 1..g.vertices
    • edges :: int
      • eges are consecutive numers 1..g.edges
    • src :: edge_index -> vertex_index
      • the source of edge j is g.src[i]
    • tgt :: edge_index -> vertex_index
      • the target of edge j is g.tgt[i]
    • where edge_index, vertex_index :: int
  • invariant: length(g.src) == length(g.tgt) == g.edges
• 2. adjacency list, g
  • data
    • vertices :: int
    • edges :: int
    • src_index :: int -> list[int]
      • the list of edges starting from vertice i (with i as source) is g.src_index[i]
    • tgt_index :: int -> list[int]
      • the list of edges ending of vertice i (with i as target) is g.tgt_index[i]
  • store the inverse images of the source and target maps
  • +: allows for easy traversal (through the neighbors of any given vertex)
  • -: less convenient to iterate though the edges and retrieve their sources and target
• it's often useful to have both src (edge's source vertex mapping) and src_index (vertex's outgoing edges mapping) fields
  • but the trouble now beomces bookkepping the consistency when modifying the graph
• we eventually wish to regard a graph as two interlinked data frames