Directed and undirected sub-graph extraction: the comparison

Now, we can present the results for each primary stimulus, where the sub-graph for each primary stimulus word is evaluated. To compare directed and undirected sub-graphs extracted for each stimulus, we shall use all data obtained in the sub-graph evaluation process, i.e.:

• - Sn: the number of nodes in the sub-graph created by the algorithm;
• - nSn: the number of non-semantic nodes in the sub-graph recognized by a sub-graph evaluation;
• - SnT: the number of network nodes (words) which were recognized both in the texts and in the sub-graph;
• - TnS: the number of network nodes (words) which are present in the texts but were rejected by the algorithm, and therefore are not present in the sub-graph.

Before we start the evaluation per stimulus, we have to show the joint results of the evaluation of 43 stimuli. To perform this analysis, we must determine the total number of nodes in the network - Nn. Table 3.1 shows the joint result for all sub-graphs based on the PAP corpus.

Table 3.1. Joint evaluation of 43 stimuli

If we look at Table 3.1 and compare the number of network nodes Nn and the sum of SnT (network nodes retrieved in the text to extract a sub-graph) and TnS (network nodes present in text but rejected by an algorithm), we can discern that only a fraction of the nodes (words) which are present in the network appear in the large text collection - 0.234 for the undirected network and 0.267 for the directed one. This score is substantially lower than the sub-graph node Sn-to-network node Nn ratio, which is 0.281 for an undirected network and 0.275 for a directed one. It can be said that these figures show the relation between the language dictionary (the network) and the use of a dictionary to produce texts. The nSn value (non-semantic nodes in the sub-graph) shows that the non-semantic nodes in sub-graphs are only 0.072 of the total sub-graph nodes, in both undirected and directed networks. This result shows both the semantic consistency of the empirically built association network, and the quality of the cautious method for building a sub-graph described in this chapter.

Finally, the difference in size of Sn, SnT and TnS may reflect the differences between the directed and undirected graph structures, which influence the use of the words of a text to extract a sub-graph. We shall provide a detailed analysis later on.