Hummon NP and Doreian P. “Connectivity in a Citation Network: The development of DNA theory” Social Networks 11: 39-63, 1989
Social Networks 11 (1989) 39-63
North-Holland
CONNECTIVITY IN A CITATION NETWORK:
THE DEVELOPMENT OF DNA THEORY *
Norman P. HUMMON and Patrick DOREIAN
University of Pittsburgh * *
The study of citation networks for both articles and journals is routine. In general, these analyses
proceed by considering the similarity of articles or journals and submitting the set of similarity
measures to some clustering or scaling procedure. Two common methods are found in bibliomet-
tic coupling, where two citing articles are similar to the extent they cite the same literature, and
co-citation analysis where cited articles are similar to the extent they are cited by the same citing
articles. Methods based on structural and regular equivalence also seek to partition the article
based on their positional location. Such methods have in common focus on the articles and
partitions of them. We propose a quite different approach where the connective threads through a
network are preserved and the focus is on the links in the network rather than on the nodes.
Variants of the depth first search algorithm are used to detect and represent the mainstream of the
literature of a clearly delineated area of scientific research. The specific citation network is one
that consists of ties among the key events and papers that lead to the discovery and modeling of
DNA together with the final experimental confirmation of its representation.
Introduction
In this paper, we develop new methods for analyzing the connectivity
in directed networks. These methods are based on search algorithms,
primarily depth first search, and an important variant, .+xhaustiue search.
Using these methods to analyze a citation network describing the
development of DNA theory, we identify a set of papers that played a
central role in the development of that theory. These papers are
identified through their structural connectivity in the network. Our
approach to the analysis of connectivity is to focus on sequences of
links and nodes, called search paths. The properties of search paths are
used to quantify various dimensions of connectivity.
* Revised version of a paper presented at the Eighth Annual Sunbelt Conference for Social
Network Analysis, San Diego, California.
* * Department of Sociology, University of Pittsburgh, Pittsburg, PA 15260, U.S.A.
0378-8733/89/$3.50 0 1989, Elsevier Science Publishers B.V. (North-Holland)
40 N. P. Hummon and P. Doreian / Connectivity in a citation network
Analyzing the connectivity of the DNA research literature
Since the pioneering work of Garfield (e.g., 1955) and its strong
reinforcement by Price (1965) one decade later, the idea of analyzing
networks among scientific events has become common place. Most
often, the events are scientific productions linked by citation so that
citation analyses, of one sort or another, are legion. “(T)he citation is a
precise, unambiguous representation of a subject that requires no
interpretation and is immune to change in terminology” (Garfield
1979: 3). Citations are explicit linkages between papers that have some
important content in common. Indeed, the idea of papers being linked
by citation forms the foundation on which the construction of the
Science Citation Index rests. While there are problems with taking
citations at face value (e.g., self-citation, negative citation, window
dressing and politically motivated flattery) there is a strong correlation
between citation rates and peer judgments that holds for many disci-
plines (Garfield 1979: 63). There are many benefits that stem from
analyzing the citation links between articles and, in aggregation, be-
tween journals. It is possible to map the intellectual content of field
and demarcate their (porous) boundaries. Interaction between fields
can be studied and an historical account of development of scientific
thought can be constructed.
The majority of citation studies, for our purposes, can be grouped
into two broad categories: those measuring the prominence, or impor-
tance, of publications and journals (within networks); and those
analyzing the structure of citation networks. Citation counts provide
some indication of the utility of a scientific production (and the
journals containing these productions). The emphasis on measures
attached to papers extends to journals and the Journal Citation Reports
give immediacy indices, half lives, and impact factors for journals.
More sophisticated and complicated measures based on the eigen
structure of a normalized citation matrix have been constructed (Pinski
and Narin 1979; Doreian 1987), although Noma (1987) suggests that
these indices add little to the information contained in raw citation
counts. For all of these measures, the structure of the network from
which they are constructed remains implicit or secondary. The primary
goal is a set of measures for nodes.
Structural analyses of citation networks emerge when the patterns of
specific network relations are considered. The obvious relations are
“cites” and its converse “cited” and various graphs depicting these
N.P. Hummon and P. Doreian / Connectivity in a citation network 4 1
relationships can be constructed for a relatively small set of scientific
events. r Garfield (1979: 81-97) reports on a set of these historiographs
which includes the DNA citation network we analyze in this paper. *
Analysis of the structure of the network regardless of whether it is
the relation “cites”, or “cited by”, or bibliometric coupling (Kessler
1963), or co-citation (Small 1973) focus on the clustering of nodes (be
they articles, journals, or scientists) on the basis of ties connecting
them. Our purpose here is to present and use a set of methods that
focus on the links of the network rather than on the nodes.
The DNA citation network
The data for our connectivity analysis are taken from Garfield, Sher
and Torpie (1964) and partially summarized by Garfield (1979). For
Fig. 1. DNA theory network.
’ In linked-list form very large networks can be sorted and analyzed but their graphs are too large
to draw and interpret.
* Of course, a primary, and crucial objective is to ensure. that the historiograph is accurate. Too
much error or noise in the historiograph, or any network for that matter. compromises any
analysis of its structure.
Table 1
The 40 milestone events of DNA research from Garfield ef al. (1964) after Asimov (1963)
Event Date Author(s) Discovery
1
2
3
4
5
6
7
8
9
10
11
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1820
1860s
1869
1880
1886
1 8 9 1
1900
1900-10
1909
1926
1928
1929
1 9 3 1
1935
1935
1936
1938
1 9 4 1
Bracconot
Mendel
Miescher
Flemming
Kossel
Fischer & Piloty
DeVries
Fischer
Levene
Muller
Griffith
Isolation of specific amino acids from protein.
Predictability of dominant and recessive traits in plants.
Isolation of nucleic acid.
Levene
Alloway
Stanley
Levene
Bawden & Pirie
Caspersson & Schulz
Beadle & Talum
Described replication of paired chromosomes within the cell nucleus.
Study of purine and pyrimidine content of nucleic acid.
Isolation and synthesization of ribose as a freely occurring sugar.
Concept that spontaneous alteration of the chromosome can lead to mutation.
Demonstration of the peptide chemical linkage of amino acids forming protein.
Identified the 5 carbon sugar ribose as a component of nucleic acid.
Produced altered genes and mutants with X-rays.
Production of living capsulated bacteria from dead capsulated pneumococci.
Discovery that certain nucleic acids contain deoxyribose (DNA).
Proof that genetic material from a dead strain influences characteristics of a live strain.
Isolated crystals of tobacco-mosaic virus.
Proposed formulae assigning linkages between the nucleotides.
Discovered the virus (cf. 14) was also a nucleoprotein.
RNA concentration is highest in cells where the rate of protein synthesis is highest.
Via X-rays produced mutant molds requiring precise amino acid supplementation.
44 N. P. Hummon and P. Doreian / Connecfiuity in a cifation network
Garfield et al. (1964: iii) “the history of science is regarded as a
chronological sequence of events in which each new discovery is
dependent upon earlier discoveries” (emphasis added). Successful re-
search is seen as a sequence of important events having a time ordered
sequence where later work is critically dependent on earlier work and
important scientific goals are achieved. Garfield et al. constructed two
historiographs stemming from Asimov’s (1963) account of the history
of DNA work in The Genetic Code. A carefully identified set of 65
specific research productions, cited by Asimov in his historical account,
were examinated. These productions were grouped into 40 milestone
events and the constructed historiographs represent these events and
the ties that link them. One is reconstructed from Asimov’s narrative
while the other was obtained by carefully examining the citations made
in each bibliography. 3 We analyze the second historiograph. Figure 1
contains the citation-based historiograph constructed by Garfield et al.
(1964: transparencies) and reviewed by Garfield (1979: 88). The rela-
tion depicted is “cites”. For each linked pair, the event on the right
cites the event to the left. 4 Table 1 lists the 40 milestone events
between 1820 and 1962.
Each event was categorized and coded into broad subject categories:
nucleic acid chemistry (NC), protein chemistry (PC), genetics (G), and
microbiology (M). The coding for each milestone event is shown in
Table 2. 5
Our purpose is to examine the links in this network with a view to
finding the main stream of research through that network.
3 If events A and B are among the milestone events, then if A cites B there is a direct connection
between the events. If C is not a nodal event, but it is the production of an author of a nodal
event, then if A cites C and C cites B there is a less direct link. Finally, if C is written by an author
not represented in any of the milestone events and the pattern is A cites C and C cites B it is an
even less direct link. In our analysis, we do not distinguish between direct and less direct citations.
4 There is a 2-cycle between 32 (Ochea) and 33 (Komberg). The arrow in Figure 1 represents the
flow of useful information rather than cites.
5 Garfield et al. note (1964: 15) the need for postgraduate level training in the field being
analyzed and, as they had project members with this training, we assume that reasonable decisions
were made throughout their analysis and that we can rest our work on their painstaking sifting of
the relevant citations.
Depth first search can also find strongly connected subgraphs, or
cycles. If a directed graph is also a DAG, it can be sorted using the
depth first search algorithm. This sort is a topological sort and orders
the nodes so that no node is before a node that points to it. Topological
sorts of DAGs are, in general, not unique.
The DNA network contains only one cycle involving nodes 32 and
33. These two papers overlapped in time, as both have 1956 publication
dates. Not surprisingly, citation networks are very nearly directed
acyclic graphs, or DAGs.
Removal of one link (the citation of event 32 by event 33) from the
DNA network, transforms it into a DAG. As the Watson and Crick
6 While in this rather simple network, these weakly connected subgraphs can be picked out
visually from Figure 1, we doubt that eyeballing techniques are useful for much larger networks.
N. P. Hummon and P. Doreian / Connecriviry in a citafion network
Connectivity procedures
1. Weakly connected subgraphs
The first task is to examine the citation network to determine whether
it has distinct subgraphs. Simple or weak connectivity in a directed
graph can be determined by symmetrizing the network, and performing
a depth first search. The DNA network contains four weakly connected
subgraphs, as can be easily seen in Fig. 1.
Subgraph 1
1 8
Subgraph 2
2 18
Subgraph 3
3 4
28 31
32 21
39 35
Subgraph 4
7
5 12 9 5 1 5 22 19 24
1 7 10 16 1 4 20 1 1 1 3 2 1
2 3 26 29 3 1 40 2 5 30 3 4
3 3 38 36
It is clear that the main root for this network starts with node 3, the
paper by Meischer written in 1871. The other subgraphs are small,
containing only one or two nodes. 6
2. Strongly connected subgraphs (cycles), and sorts
46 N.P. Hummon and P. Doreian / Connectivity in a citation network
research is cited by Ochoa (who cites two other events) and Komberg
cites only Ochoa, this is a reasonable choice. 7 Given DAG, we can
analyze either “cited-by” or “cites” (or both). Here, the network is
transposed so the links are is-cited-by relations as this form of the
network is directed forward through time, and represents the influence
patterns and dependency relations in a citation network. The following
topological sort order was found for the DNA network.
Sort Order DNA Network
26
2 3
19
14
1 1
1 0
I
6
3
2 5
21
1 5
22
36
33
3 8
4
2
24 28
1 6 3 1
13
1 7 34
9
5 12
29
21
40
35
1 8
8
32
39
The depth first search procedure outputs nodes in the listed order
starting with 26, 23, 19, 24, etc. and ending with 4, 2, 18, 1, and 8. We
have broken the sorted list into sub-sequences of connected paths so
that the structure of the network is easier to see. Recall that the relation
used to sort the network is one of dependency. Node B follows node A
if it is dependent on node A. Figure 2 presents the dependency
structure of the core of the network starting from the root node 3.
The core of the network begins with node 3 and ends with node 38.
Nodes 26, 23, 6, 9, etc. are all prior to root node 3 because they have no
dependency relation with node 3. Nodes 4, 2 and 18, and 1 and 8 are
the separate subgraphs identified ‘above. Note that the order of nodes
37, 36, 40 and 38 could be interchanged in the sort list changing the
dependency relations. It is in this sense that the sort order of the
’ An alternative is to collapse events 32 and 33 into a single node.
N.P. Hummon and P. Doreian / Connectivity in a citation network 41
Table 2
The milestone events coded by research area
Event Protein
chemistry
Genetics Nucleic
chemistry
Microbiology
J1
2
3
4
5
6
7
8
9
1 0
1 1
12
1 3
14
1 5
16
1 7
1 8
1 9
20
2 1
2 2
23
24
2 5
26
21
28
29
3 0
3 1
32
3 3
34
3 5
3 6
31
38
39
40
J
J
J
–
i
J
–
J
–
J
J
J
J
J
J
J
N.P. Hummon and P. Doreian / Connectivity in a citation network
J-5-l~l-z2-27-32
I-,, t4a r”33-35
l-38
Fig. 2. Dependency structure of core of network (based on topological sort).
network is not unique; a very large number of alternative lists could be
constructed using such changes.
3. Connectivity and path lengths
Another way to examine connectivity in these networks is to compute
the path distances between node pairs. The distance of most interest in
analyzing connectivity is the longest path or detour between each pair
of nodes. This computation is accomplished with an important variant
on the depth first search algorithm, the exhaustive search algorithm.
Briefly, the exhaustive search algorithm finds all possible search paths
through the network. To compute the maximum distance, it is only
necessary to record the maximum distance for each node pair across all
possible search paths emanating from the start node.
The maximum path distance for the DNA network is 10 links. Six
out of 676 search paths are of length 10, including two search paths
emanating from the root node. The longest paths from the root node to
all other nodes are given in Table 3.
Table 3
DNA Network
Maximum path distance from node 3
Node Distance Node Distance Node Distance Node Distance
4 1 5 1 1 2 2 1 5 3
20 3 21 4 22 5 2 5 4
2 7 6 2 9 4 30 4 3 2 7
3 3 8 3 5 9 3 6 8 31 8
3 8 1 0 3 9 1 0 40 9
N.P. Hummon and P. Doreian / Connectivity in a citation network 49
Table 4
Main path sort order compared with longest path distance
Node Order Node Order Node Order Node Order
3 0 5 1 1 2 2 20 3
30 4 2 5 4 2 1 4 1 5 3
2 9 4 22 5 21 6 3 2 I
3 7 8 3 6 8 40 9 3 3 8
3 5 9 39 1 0 3 8 10
The longest path vector corresponds very closely to DAG sort order
reported above. Repeating that portion of the sort order represented in
Figure 2, we see that only the longest path distances for nodes 15 and
33 depart from the expected order, and both these are at distances only
one link different from their implied sort order values in Table 4.
Figure 2 shows that both nodes 15 and 33 could be interchanged
with other nodes to change their order to the expected value. However,
such changes would move other nodes out of their expected order.
4. Network connectivity and search paths
We propose a new index of link connectivity based on the measure of
traversal counts in search paths through the network. The construct
this index, we propose three related operationalizations.
First, suppose we extract the subgraph from the network in Figure 1
that represented all possible paths from node 3 to node 22. It would
look like Figure 3.
If there are N nodes in the subgraph, there exist N( N – 1) possible
subgraphs connecting all directed node pairs in the network. For the
graph in Figure 3, only 19 of the possible 42 node pairs have connect-
;!:+
5 1 2
Fig. 3. Graph of all links from node 3 to node 22.
5 0 N.P. Hummon and P. Doreian / Connectivity in a citation network
ing links and paths. Thus, we can construct subgraphs that connect the
node pairs:
3- 5 3-12 3-15 3-20 3-21 3-22
5-12 5-15 5-20 5-21 5-22
12-15 12-20 12-21 12-22
15-22
20-21 20-22
21-22
To compute the traversal counts for each link, we construct the
adjacency matrices for all the subgraphs connecting these node pairs.
These matrixes can be “stacked” by corresponding row and column
nodes. The traversal counts of interest are the projected counts of all
links connecting node pairs projected onto a base matrix. ’ The result-
ing projection matrix contains counts of the number of times each link
was involved in connecting all node pairs using all subgraphs derived
from the network. We call this the node pair projection count (NPPC)
method of generating traversal counts. The network is presented as a
graph valued by traversal counts. For Figure 3 this is:
3: 5 (6) 21 {2}
5: 12 (10)
12: 15 (6) 20 {9)
15: 22 (4)
20: 21 {8} 22 (4)
21: 22 (5)
The link with the highest traversal count of 10 is 5-12. This means
that this link was a member of 10 of the 19 subgraphs that connect all
node pairs. Links that bypass several nodes, such as 3-21 generate low
traversal counts. Traversal counts reflect the connectivity that both
precedes and follows a link in a search path.
We propose two other ways of computing link traversal counts, and
both are based on the exhaustive search algorithm. As noted above, this
algorithm generates all possible search paths through the network
emanating from an origin node. The count of the number of times a
link is traversed by all possible search paths is a simple way measure of
the importance of that link. We label this the search path link count
’ Cf. projecting back along the time axis to the phase space for a dynamic system.
N.P. Hummon and P. Doreian / Connectivity in a citation network 5 1
(SPLC) method of computing traversal counts. The traversal counts
computed by the SPLC method for the simple network in Figure 3 are:
3 : 5 ( 3 ) 2 1 (11
5 : 12 ( 6 )
12: 1 5 ( 3 ) 20 ( 6 )
15: 22 ( 4 )
20: 2 1 ( 4 ) 22 ( 4 )
21: 22 ( 6 )
22:
The third method is also based on the set of all search paths
emanating from a start node, but instead of simple link counts, it
accounts for all connected node pairs along the search paths. Thus a
link in the middle of a search path will receive a higher traversal count
than links at the ends of the search path because “inner” links are
involved in connecting more node pairs than links at the beginning or
the end of a search path. We label this the search path node pair
(SPNP) method of computing traversal counts. The traversal counts
using the SPNP method for the network in Figure 3 are:
3 : 5 (13) 21 (2)
5: 12 (20)
12: 15 (6) 20 (15)
15: 22 {4}
20: 21 (8) 22 (4)
21: 22 (6)
22:
These traversal counts are analogous to counts of the number of
geodesics that run through a node in Freeman’s (1978) centrality
measure. However, we are concerned with the connectivity of links
rather than the centrality of nodes. There is an obvious duality between
the centrality of nodes and the connectivity of links.
For the DNA network, the maximum traversal counts and links for
the three methods are: search path link count for link 27-32 is 328;
search path node pair for link 22-27 is 1178; and node pair projection
method for link 27-32 is 152. All three methods identify the same pair
of links with the two highest counts in the network. The 22-27 link
connects the Chargaff paper to the Watson and Crick paper, and the
27-32 link connects the Watson and Crick to the Ochoa paper.
These traversal counts can be used in another important way: they
define the main path through the citation network. We can use the
traversal counts to determine a search path through the network that
52 N.P. Hummon and P. Doreian / Connectivity in a citation nerwork
reflects the greatest connectivity in the network. At any node, we
choose the next link in the path as the outgoing link with highest
traversal count. By repeatedly applying this choice rule, we define a
path through the network that follows a structurally determined most
used path. This link selection technique is an example of a priority first
search algorithm, where the priority is set by the traversal counts. It is
our intuition that the main path, selected on the basis of the most used
path will identify the main stream of a literature.
For the DNA network, a traversal count priority first search identi-
fies the same search path for all three methods of generating traversal
counts. Thus the DNA network main path contains the following
Node Paper
3 Miescher, 1871
5 Kossel, 1886
12 Levene with Mori and London, 1929
20 Avery, MacLeod and McCarty, 1944
2 1 Chargaff, 1947
22 Chargaff, 1950
27 Watson and Crick, 1953
3 2 Ochoa, 1955-1956
3 6 Hurwitz, 1960
40 Nirenberg and Matthaei, 1961-1962
Figure 4 shows the main path superimposed over the network.
Fig. 4. DNA main stream.
N.P. Hummon and P. Doreian / Connectivity in a citation network
5’. The network of main paths
The analysis reported above reports the main path starting with node 3.
There are sound reasons for this choice, both from other connectivity
analyses, and other findings reported below. However, what happens if
this assumption is relaxed, and all nodes in the network are selected as
start nodes of a main path analysis? Table 5 reports the results of such
an analysis.
Table 5
The set of all main paths in the DNA network (based on SPNP traversal counts)
start
node
Main path
1
2
3
5
6
9
10
1 1
1 2
1 3
1 4
1s
1 6
1 7
19
2 0
21
2 2
2 3
2 4
2 5
2 6
2 7
2 9
3 0
31
3 2
33
3 4
35
3 6
8
51220212227323640
18
12 20 2122 27 32 36 40
91220212227 32 3640
1220212227 32 3640
1720212227 323640
1320212227 32 3640
20212227 323640
20212221323640
1617 2021222732 3640
2227 32 3640
1720212227 323640
20212221323640
2227323640
212221323640
2227 323640
27 32 3640
27 32 3640
28
40
27 32 3640
323640
32 3640
40
32 36 40
36 40
35 38
40
38
40
54 N.P. Hummon and P. Doreian / Connectivity in a citation network
Thirty-one of the forty nodes have outgoing links, and therefore can
be used as start nodes for the analysis. Table 5 shows that, when
considering the node specific main paths, only four nodes result in
main paths that do not join the main path that emanates from node
three. Of these four, two are part of subgraphs that are not even weakly
connected to the main network: these are nodes 1 and 2. The remaining
nodes, 24 and 35, are directly connected to terminal nodes 28 and 38
respectively, and none of the main path nodes are reachable from these
nodes. Thus, virtually all start nodes have main paths that converge to
the main path from node 3, and for the exceptions it is impossible to
reach the main path. Connectivity in this citation network converges to
the main stream of this literature.
We now discuss the significance of this sequence of scientific events
from other perspectives.
Corroborative evidence
Citation importance
DNA was discovered in 1869 by Miescher (node 3) so that this node
has to be non the main path: it is.
Asimov (1963) identified event 20 (the discovery by Avery et al. that
dexyribonucleic acid (DNA) carries genetic information that was capa-
ble of transforming one bacteria strain into another from which the
DNA was extracted) as truly critical. Garfield et al. (1964) constructed
a weighting scheme. so that events can be measured in terms of the
types of ties (direct, strong indirect, and weak indirect with each
successive type of tie being weighted less) incident to them. According
to their index, event 20 has the greatest nodal weighting. It is reasona-
ble to expect that such a key event be on the main path: it is. We know
that Watson and Crick (event 27), together with Wilkins, shared a
Nobel Prize for their work and that Ochoa (event 32) shared a Nobel
Prize with Komberg (event 33). Such prize winning events should be on
the main path: they are. 9 Garfield et al. (1964: Appendix II) give the
9 Events 33 and 32 have a reciprocal link between them. As Ochoa’s work was drawn on explicitly
by event 40, our main path has only event 32. Wilkins (node 26) shared the Nobel Prize with
Watson and Crick (node 27). His development of X-ray diffraction was critically important and
the “main path” from node 26 leads immediately to the main path of the network. Methodological
breakthroughs and new conceptual developments (node 23) may have this ancillary standing of
being just off the main path in citation networks.
N.P. Hummon and P. Doreian / Connectivity in a citation network 5 5
nodal weighting value for each nodal event. Starting with the highest
weighting value and stopping when one of the terminal nodes is
encountered, the set of nodes with the highest weighting values are, in
descending order of the weighting index, event 20, event 32, event 22,
event 21, event 36, event 27, and event 40. A strong criterion of
adequacy is that all of these nodes with the highest nodal index be on
the main path: all of them are.
The dominant field via Q-analysis
The data in Table 2 contain the coding of the milestone events by
research area. Let A be matrix obtained by having a value of 1 where
there are check-marks and a value of 0 where there are dashes. Atkin
(1977) presents a systematic methodology whereby the structure of
such a matrix can be explored. Each research area becomes simply the
set of events containing its content while each event is represented by
the research areas it contains. Each research area becomes a simplex
and together they form a family of simplexes. Similarly, each event is a
simplex made up of its own content areas and together they form a
family of simplexes. These, together with their faces, form dual simpli-
cial complexes. We consider the one concerning the family of research
areas.
With A the data matrix, its transpose is A’. The product A’A gives a
4 X 4 matrix expressing the extent to which the research areas overlap.
The overlap is the number of events containing both research areas and
is referred to as a (common) face. A (modified) lo Q-analysis consists
of an exploration of the connective structure of common faces. Table 6
gives the relevant details.
The top panel of Table 6 shows the shared face matrix (where the
entries express the size of the overlap rather than the dimension of the
face). Nucleic chemistry is found in 26 of the 40 milestone events.
Similarly, protein chemistry is found in 12 events, genetics in 11 events,
and microbiology in 4 events. The off diagonal elements give the
number of events where pairs of research areas are both present. Thus,
of the 26 nucleic chemistry events, six share protein chemistry content,
while five share genetic content. Similarly, nucleic chemistry shares
lo If U is a 4 x 4 matrix of ones, a Q-analysis uses the matrix A’A-U. We ignore CJ, but continue
to use q as a notation.
5 6 N.P. Hummon and P. Doreian / Connectivity in a citation network
Table 6
Q-analysis of DNA content complex
(a) Sharedfa?e * matrix
Protein chemistry PC
Genetics G
Nucleic chemistry NC
Microbiology M
PC
1 2
1
6
0
G NC M
1 1
5 26
0 3 4
(b) Q-analysis
Values of q
26-13
Complexes
(NC)
Qq
1
12 ~NCj(PC) 2
11-7 WIPWG) 3
6 (NC,PC}(G) 2
5 (NCJ’CG) 1
4 {NCJ’CG){M) 2
3 (NCJ’CGM} 1
(c) Graphs of equivalence classes
M
PC-NC-G
q=5.
N’C
P C ’ ‘G
q=3
three events with microbiology. A Q-analysis proceeds by considering
progressively smaller values in the shared face matrix. For a given value
of q the complexes present in the Q-analysis form equivalence classes.
For values of q = 26 through 13 there is a single equivalence class made
up of nucleic chemistry. For q = 12 there are two separate equivalence
classes made up of nucleic chemistry and protein chemistry. These
equivalence classes are shown in the middle panel of Table 6 and the
right hand column simply counts the number of equivalence classes
present. For q = 11 through 7 there are three equivalence classes each
containing a singleton: nucleic chemistry, protein chemistry and genet-
ics. For q = 6 nucleic chemistry and protein chemistry join (as there are
6 events sharing their content) while genetics remains in a separate
equivalence class. For q = 5 all three join in a single equivalence class.
For q = 4 the area of microbiology joins the set of complexes but it is
disjoint. Finally, for a q = 3 all areas are linked together in a single
equivalence class. The third panel of Table 6 gives pictorial represen-
N.P. Hummon and P. Doreian / Connectivity in a citation network 51
tations of the single equivalence classes found for q = 5 and for q = 3.
For q = 5, nucleic chemistry is the subject area linked to both protein
chemistry and genetics. For q = 3 nucleic chemistry is again the core
having separate links to protein chemistry, genetics and microbiology.
None of the other areas are connected directly. It is very clear that
nucleic chemistry forms the core of the DNA content complex. Given
its importance, it ought to be present on the main path. Indeed, all of
the events of the main path have nucleic chemistry as all or part of
their content.
Both the weights assigned by Garfield et al. and the central core
identified via a (modified) Q-analysis provide corroborative evidence
for the identification of the main path. The seven nodes with the
highest nodal weighting are all on the main path, and with nucleic
chemistry being identified as the core of the research specialty.
A comparison with equivalence approaches
We have shown that other paths, beyond the main path, can be picked
out in the network. Event 2 could be taken as a start point although the
path would reach only event 18. Each of events 10 and 11 can be taken
as a start point and paths can be traced that reach one or more of the
terminal events. The emphasis on connectivity is on the strands that
connect the research productions that cumulate in a clearly identified
research specialty. The objectives of clustering citation networks is
quite different and can be seen as a complementary analysis.
There are two broad approaches to the clustering of citation net-
works: one is found in citation analysis; the other stems from the idea
of equivalence found in the social network literature. In the citation
analysis literature, the citation relation has been clustered directly (for
example, Narin et al. 1972; Carpenter and Narin 1973).
Two further network relations have been constructed from these
citation patterns. Kessler (1963) suggested the idea of bibliometric
coupling whereby two articles are similar to the extent that they share
citation to common sources. As defined, a bibliometric coupling rela-
tion is entirely static and the similarity is defined in terms of the
authors’ bibliographies. Yet scientific fields are dynamic and Small
(1973) defined a new form of document coupling in the form of
co-citation to, in part, reflect this. Two articles are similar to the extent
5 8 N.P. Hummon and P. Doreian / Connectivity in a citation network
they are jointly cited by subsequent authors. “Co-citation patterns
change as the interests and intellectual patterns of the field change”
(Small 1973: 265). Moreover, they “can be used to map out in great
deal the relationship between key ideas” (Small 1973: 266). It is
primarily through the creative use of co-citation analysis that the
content of fields can be mapped and the interactions between them
studied. Longitudinal study of co-citation analysis permits a dynamic
picture depicting the emergence of fields and specialties.
Once co-citation has been defined and measured for pairs of articles
in a network, the major data analytic tool is cluster analysis. Moreover,
by virtue of the gigantic size of the networks usually considered,
computational constraints have limited the analyses primarily to single
link clustering, even though it is prone to producing string-like clusters.
Nevertheless, Small and Griffith (1974) and Griffith et al. (1974)
employed this tool to map out the structure of science in terms of its
diverse fields and specialties. Sets of coherent clusters were established,
solely on the basis of the pattern of co-citation, that correspond to
clearly defined scientific areas. The mosaic of science is depicted in
terms of clusters, each representing a research specialty or field, and a
network linking the clusters. Small’s (1977) longitudinal study of the
collagen research specialty showed the emergence and change of a
specific field. Many other co-citation analyses have been conducted
and the idea of co-citation has been extended to co-word analysis (e.g.
Callon et al. 1983) whereby scientific productions are similar to the
extent they share the same key words, or words in their titles.
In the social network analysis formulation of equivalence consider-
able attention has been focussed on representing and homomorphically
reducing networks. The initial formulation is found in Lorrain and
White (1971) where, loosely, two objects are structurally equivalent if
they are connected to exactly the same other objects. If we consider the
relation cited by, then structural equivalence maps directly into co-cita-
tion: two articles are structurally equivalent if they are cited by the
same other articles. ‘i With regard to citing, structural equivalence
appears to map into bibliometric coupling. Both the relations, cites and
cited, can be analyzed simultaneously, in which case articles are struct-
urally equivalent if they cite the same sources and are cited by the same
” Indeed, Small’s measure of the extend to co-citation could be a useful measure of structural
equivalence.
N.P. Hummon and P. Doreian / Connectivity in a citation network 59
subsequent articles. Block modeling tools have been used in the soci-
ology of science (for example, Breiger 1976 and Lenoir 1979) suggests
their use in co-citation analysis. This being the case, algorithms such as
CONCOR (Breiger et al. 1975) or STRUCTURE (Burt 1976, 1987)
may be useful. In the context of journal networks, Doreian and Fararo
(1985) and Doreian (1985) have used Burt’s algorithm to cluster jour-
nals into coherent clusters. A generalization of structural equivalence is
regular equivalence where, again loosely, two objects are regularly
equivalent if they are connected in equivalent ways to equivalent
objects (White and Reitz 1983). Such a generalization may be particu-
larly useful for studying multidisciplinary networks.
Given the time ordering of the citations and that, with the exception
of a single two-cycle, the network is a directed acyclic graph with
multiple start points, regular equivalence is the most relevant defini-
tion. The expectation is that such an analysis will pick out intellectual
generations in the citation network. Figure 5 gives the regular equiv-
alence dendrogram for the citation network of Figure 1.
Event 7 is picked out as the isolated node in the network. Events 1,
2, 3, 6, 10, 11, 14, 23, and 26 belong to a cluster that can be viewed as
the first generation events for the research area. All are events that can
be viewed as bringing genuinely new information to the research area.
It includes all of the early events such as the Bracconot event in 1820.
It also includes event 23 where Pauling and Corey propose the concept
of a helical configuration for polypeptides chains and Wilkins’ develop-
ment of X-ray diffraction methods for the study of nucleic acid. Both
are events that Watson and Crick build upon in constructing their
critically important spatial model of DNA.
A second cluster is made up of events for, 8, 18, 28, 37, 38, 39, and
40. All can be viewed as terminal events and they appear to fall into
two categories: capstones and deadends. It appears that the research of
event 8 lead nowhere according to the citation network, as did research
contained in events 4, 18, and 28 which can all be viewed as deadends.
However, the research contained in events 37, 38, 39, and 40 can all be
seen as capstones on which future research can be built.
A third cluster is made up of the events 24, 25, 32, 33, 34, 35, and 36.
With one exception (event 33) these form the last but one generation as
they are one step away from terminal nodes. The further cluster of
events can be viewed, in the main, as the second generation of events
one step away from the first generation events. In the middle portion of
60 N. P. Hummon and P. Doreian / Connectivity in a citation network
C O M P L E T E L I N K A G E METHOD ( F A R T H E S T NEIGHBORI
T R E E D I A G R A M
-1 .000
13
9
16
5
31
2 0
17
15
12
29
27
21
22
24
3 4
3 0
25
3 6
3 5
3 3
3 2
28
3 9
3 8
4 0
3 7
18
6
4
7
2
1
2 6
23
10
14
11
19
6
3
DISSIMILARITIES
1 .000
Fig. 5. Dendrogram for regular equivalence clustering.
N.P. Hummon and P. Doreian / Connectivity in a citation network 6.
the network there is some confusion as different events are at different
distances from the initial and terminal events. Regular equivalence does
pick out the intellectual generations, ignoring the time dimension – so
that Wilkins’ work of 1953 is regularly equivalent to Miescher of 1869
– in a fairly coherent fashion. It is also clear that partitioning the
network in terms of intellectual generations collapse together the paths
that can be traced from the initial work to the terminal work.
Conclusion
The citation network that describes the important events in the devel-
opment of DNA theory has been subjected to a variety of analyses.
First, the network was sorted, and an ordered set of nodes were
identified by their dependency relations. This set begins with node 3
and includes nodes to all the other nodes on the main p,ath. Next, the
longest path analysis was reported, and the same basic set of nodes was
identified. Third, the connectivity measure of traversal counts was
introduced. The highest traversal counts fall along this same connected
set of nodes. To formalize this observation, a priority first search was
used to trace the main path from node 3. Finally, when all possible
main paths were generated, there is a tendency for connectivity to
converge the main path, and then follow it.
:
Using a completely different methodology, other researchers -had
already identified the events that make up the main path as the most
significant in the development of DNA theory. Thus our formal
connectivity analysis employing network search techniques is com-
pletely consistent with the analysis of other researchers.
In summary, three widely different methodologies come to the same
general conclusion about the structure of the DNA network, and, more
importantly, about the social process by which this exciting field
developed.
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