## Edge & Arc Lists

Edgelists represent ties as dyadic information, as a pairwise listing of each of the relationships present in a network. Edge lists remove the unnecessary storage of all of the absent relationships in a network (the 0s in an adjacency matrix). The convention is that node pairs in an edgelist represent the senders in the first column, with the receivers in the second column. “Edges” typically refer to undirected networks (and are represented by lines without arrowheads in graph visualizations), while the corresponding version for a directed network is typically referred to as an arclist (“arcs” denoting directed ties, generally represented in graphs as lines with a single arrowhead pointing from the sender to the reciever of a tie). Table 6.5 presents the same directed network data from Table 6.4 that correspond with Figure 1.1.

Table 6.5: Directed, Binary Network in Arclist Format.
snd rcv
1 2
1 3
2 4
3 2
3 4
3 5
4 1
4 5
4 7
4 8
6 5
7 4
7 8
8 4
8 7

An important limitation of edgelists is that any isolates in the network are not identifiable from the edgelist itself (note the absence of node 9 in Table 6.5. For that reason, edgelists are generally coupled with an additional data file. These are generally where node attribute data are stored. Alternatively, some computational formats that rely on edgelists will ask for a separate specification of the number (and IDs) of nodes in the network independently from the edgelist (i.e., defining the nodeset).

When drawing networks from data, or filling out one of these table formats from a figure, an easy check (on small networks like these) is to count up the number of ties in the Figure (15 for the example being used above), or the number of 1s in the matrix (limited to the top half if for an undirected network), or the number of rows/edges in the arclist.

The details above thus far have focused only on binary network data. If instead the networks are weighted, these formats can readily be adapted to incorporate the weight information. In adjacency matrices, the weights can replace the binary entries (the 1s can be replaced with the values. In arc lists, the weights generally are simply added as a third column. So a row of {2, 1, 5} would indicate a tie of weight 5 from node 2 to node 1.118