# Stratigraphic Graphs

## N. Frerebeau

### 2026-06-23

    library(aion)
    library(igraph)

A stratigraphic graph represents the directed relationships between temporal units (archaeological deposits), from the most recent to the oldest (Harris 1997). It can be formally defined as a directed acyclic graph (DAG), in which each vertex represents a layer and the edges represent stratigraphic relations.

# 1 From an edge matrix

At the most basic level, stratigraphic relations can be captured in a two-column `matrix` (or `data.frame`) of edges, where each row represents a relation element.

    ## Harris 1997, fig. 12
    harris <- data.frame(
      X = c(1, 1, 1, 2, 3, 4, 5, 6, 6, 7, 8),
      Y = c(2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 9)
    )

This table of relations can then be used to create a graph. Note that these relations are to be read from the top of the stratigraphic sequence to the bottom (“X is above/later than Y”), but the reverse is possible by changing the `direction` argument in `graph_create()`.

    ## Create a graph object
    g <- graph_create(harris, direction = "above", type = "stratigraphy")

Multiple edges and loop edges may need to be removed, as well as redundant relations (by transitive reduction):

    ## Remove redundant relations
    g <- graph_prune(g)

Finally, the graph can be plotted with an appropriate layout:

    plot(g, layout = layout_with_sugiyama)

plot of chunk plot

# 2 From time intervals

A stratigraphic graph can also be used to represent temporal relations (posteriority) within a set of time intervals:

    ## Seven time intervals expressed in years CE
    int <- intervals(
      start = c(1, 2, 3, 6, 9, 13, 17),
      end = c(7, 4, 15, 14, 11, 18, 19),
      calendar = CE(),
      names = c("A", "B", "C", "D", "E", "F", "G")
    )

    ## Create a stratigraphic graph
    strati <- graph_create(int, type = "stratigraphy")

    ## Remove redundant relations
    strati <- graph_prune(strati)

Equivalence relations (i.e. at least partial contemporaneity) can also be represented with an interval graph:

    ## Create an interval graph
    inter <- graph_create(int, type = "interval")

These two graphs therefore capture all temporal relations:

    ## Stratigraphic graph
    plot(strati, layout = layout_with_sugiyama)

    ## Interval graph
    plot(inter)

plot of chunk graphs

# References

Harris, Edward C., 1997. Principles of Archaeological Stratigraphy. Seconde edition. Academic Press.