Adding the Topical Guide and Index
Our analysis so far has focused on cross-references between verses. This post expands the cross-reference graph by including topics from the Topical Guide (TG) and Index to the Triple Combination (ITC).
For convenience, I am treating each topic as an additional node in the graph, with edges pointing to and from specific verses. We could imagine doing something more elaborate like creating edges between all pairs of verses referenced by a topic, but that would exponentially increase the number of edges and lose some of the structure provided by the topical organization.
There are 3512 entries in the Topical Guide, and a further 3059 entries in the Index, for a total of 6571 topics. After adding these topics and their references to the graph, we have:
| Nodes | |
|---|---|
| Verses | 41,995 |
| TG | 3512 |
| ITC | 3059 |
| 48,566 | |
| Edges | |
|---|---|
| Verse→Verse | 45,985 |
| Topic→Verse | 100,597 |
| Verse→Topic | 22,223 |
| Topic→Topic | 14,267 |
| 183,072 | |
Reference Counts
Although the number of topics is small compared to the number of verses, adding the topic references nearly quadruples the number of edges in the graph. As a result, the distribution of reference counts is dramatically shifted relative to the original graph that did not include any topic nodes:
Notably, the proportion of singletons—verses that are never referenced—has dropped from 56% to 31%, and there are significantly more highly-cited verses. If we dive deeper into the absolute and relative reference counts for each volume of scripture, we see an explosion in cross-reference coverage (the original values from the verses-only graph are shown in blue and orange):
The Pearl of Great Price retains its position as the volume with the highest relative reference count with an average of more than nine references to each verse. The Book of Mormon overtakes the Old Testament as the volume with the highest number of references overall, with more than 43,000.
Graph Components
Even with the additional nodes and edges from the Topical Guide and Index, many of the nodes in the graph are singletons or part of very small components. Isolating the largest component, as we did previously, leaves us with a subgraph containing 68% of the verses in the full graph (the largest component in the topic-free graph only covered 36% of verses):
| Nodes | |
|---|---|
| Verses | 28,573 |
| TG | 3180 |
| ITC | 2986 |
| 34,739 | |
| Edges | |
|---|---|
| Verse→Verse | 45,070 |
| Topic→Verse | 100,537 |
| Verse→Topic | 22,223 |
| Topic→Topic | 14,266 |
| 182,096 | |
Centrality
With our newly expanded graph, we can repeat the centrality analyses to identify the most “important” nodes. The Topical Guide dominates here, due to a small number of topics receiving many references from verses throughout the Standard Works as well as other topics (via “see also” lists).
| Verse | Rank (Degree) |
Rank (PageRank) |
|---|---|---|
| TG Faith | 1 | 1 |
| TG Righteousness | 1 | 2 |
| TG Repent, Repentance | 3 | 11 |
| TG Prayer, Pray | 4 | 5 |
| TG Obedience, Obedient, Obey | 5 | 30 |
| TG Sin | 6 | 27 |
| TG Jesus Christ, Prophecies about | 7 | 4 |
| TG Jesus Christ, Atonement through | 8 | 20 |
| TG Forgive, Forgiveness | 9 | 12 |
| TG God, Spirit of | 10 | 13 |
| TG Idolatry, Idol | 11 | 3 |
| TG Treasure | 11 | 8 |
| TG God, Omniscience of | 14 | 9 |
| TG Grace | 15 | 10 |
| TG Disobedience, Disobey | 17 | 7 |
| TG Angels | 29 | 6 |
Since the most important nodes all come from the added topics, these results are difficult to compare to the measurements for the verses-only graph. However, if we ignore topics and instead focus on the top-ranked verses, we can examine whether the underlying verse-to-verse structure has changed. In the table below, each centrality rank is reported as both a raw value (with topics) and an adjusted value (without topics).
| Verse | Rank (Degree) |
Rank (PageRank) |
||
|---|---|---|---|---|
| D&C 132:19 | 146 | 1 | 566 | 41 |
| Moses 6:57 | 151 | 2 | 386 | 6 |
| Mosiah 3:19 | 159 | 3 | 366 | 4 |
| 1 Ne. 19:10 | 159 | 3 | 406 | 7 |
| D&C 13:1 | 159 | 3 | 433 | 12 |
| D&C 17:1 | 169 | 6 | 326 | 1 |
| 1 Ne. 17:35 | 180 | 7 | 416 | 9 |
| Mosiah 3:5 | 180 | 7 | 523 | 28 |
| Mosiah 4:26 | 192 | 9 | 345 | 3 |
| D&C 1:16 | 212 | 10 | 471 | 15 |
| D&C 1:38 | 252 | 17 | 343 | 2 |
| D&C 1:14 | 275 | 20 | 409 | 8 |
| 2 Ne. 9:28 | 321 | 29 | 418 | 10 |
| Hel. 12:3 | 436 | 69 | 375 | 5 |
Ten of the 13 verses reported for the verse-only graph are repeated here; only 2 Ne. 9:37, 2 Ne. 25:20, and D&C 88:63 are missing. Of these, 2 Ne. 25:20 (#13 by degree) and D&C 88:63 (#14 by PageRank) are just below the top-ten threshold, while 2 Ne. 9:37 is significantly downweighted in the expanded graph (#1692 and #87 by degree and PageRank, respectively). Four new verses appear in this: Mosiah 3:5, Mosiah 3:19, D&C 13:1, and D&C 132:19. Of these, only Mosiah 3:19 is close to the threshold in the original verse-only graph (#12 by PageRank).
Hubs and Authorities
We can likewise repeat the HITS analysis from before to identify “hub” and “authority” nodes in the expanded graph:
| Hubs | Rank | Authorities |
|---|---|---|
| ITC God | 1 | 2 Ne. 31:21 |
| ITC Jesus Christ | 2 | Moses 6:57 |
| TG Spirit | 3 | Isa. 9:6 |
| ITC Name of the Lord | 4 | D&C 68:25 |
| ITC Jesus Christ—Son of God | 5 | Moro. 10:4 |
| TG Know, Knew, Known | 6 | Jacob 4:5 |
| ITC Repentance, Repent | 7 | 2 Ne. 19:6 |
| ITC Spirit, Holy/Spirit of the Lord | 8 | D&C 13:1 |
| TG Power, Powerful | 9 | TG Repent, Repentance |
| ITC Faith | 10 | Moses 6:59 |
All the hubs are from the Topical Guide or Index, which isn’t surprising given the number of outgoing edges for most topics. What is surprising, however, is that none of the top authority nodes from the verse-only graph are repeated; the highest rank for any previously identified authority node is 27 (Mosiah 7:27).
The newly identified authorities contain some of the most powerful prophecies of the coming of the Messiah in all the Standard Works. For instance, both Isa. 9:6 and 2 Ne. 19:6 prophesy of his birth (“For unto us a child is born…”). Moses 6:57, Moses 6:59, and D&C 68:25 lay out basic gospel principles and emphasize teaching them to children. One topic is included as an authority on this list, and it is one of the most doctrinally important topics of all: repentance.
Thus we see
Adding topics to the cross-reference graph significantly expands the number of connections and gives us new insights into the graph structure of the full Standard Works. In a sense, the Topical Guide and other study helps are cross-reference appendices—places to store all the cross-references that wouldn’t fit on the pages of the printed scriptures. They also serve as an abstraction of the scriptures over time and space, helping us to see patterns in the Standard Works across many authors and cultural contexts.
Some readers may be concerned that the verses ranked “most important” can change depending on the analysis method or whether topics are included in the graph. In my opinion, this variability highlights rather than obscures the beauty of the cross-references and their patterns. Just as individuals may approach the scriptures from different angles and gain different insights from the same verses, the various methods used here emphasize different aspects of the connections between verses while consistently pointing to Jesus Christ and the restoration of the gospel.
The code used for the analysis and figures in this post is available on GitHub.
© Copyright 2020–2022 Steven Kearnes. This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License .