Graph Theory Analysis of Semantic Fluency in Russian–English Bilinguals

Abstract

Background:

Semantic category fluency is a widely used task involving language, memory, and executive function. Previous studies of bilingual semantic fluency have shown only small differences between languages. Graph theory analyzes complex relationships in networks, including node and edge number, clustering coefficient, average path length, average number of direct neighbors, and scale-free and small-world properties.

Objective:

To shed light on whether the underlying neural processes involved in semantic category fluency testing yield substantially different networks in different languages.

Method:

We compared languages and methods using both network analysis and conventional analysis of word production. We administered the animal naming task to 51 Russian–English bilinguals in each language. We constructed network graphs using three methods: (a) simple association of unique co-occurring neighbors, (b) corrected associations between consecutive words occurring beyond chance, and (c) a network community approach using planar maximally filtered graphs. We compared the resultant network analytics as well as their scale-free and small-world properties.

Results:

Participants produced more words in Russian than in English. Small-worldness metrics were variable between Russian and English but were consistent across the three graph theory analytical methods.

Conclusion:

The networks had similar graph theory properties in both languages. The optimal methodology for creating networks from semantic category fluency remains to be determined.

Testing verbal fluency is a standard part of neuropsychological testing and is sensitive to early changes in brain function in many disease states, including Alzheimer disease (AD), Parkinson disease, and schizophrenia, and with norms for both children and adults (Duff Canning et al, 2004; Gomez and White, 2006; Morris et al, 2006; Sauzéon et al, 2004; Tombaugh et al, 1999). Types of verbal fluency include lexical fluency (eg, words beginning with the letter F) and semantic fluency (eg, items from a specific category, such as animals, vegetables, or articles of clothing). Verbal fluency testing is generally tested over a short time interval, most often 60 seconds, although intervals up to 10 minutes have been reported (Rosen et al, 2005). The medical literature has often focused primarily on the animal naming task, which is a large category with an estimated lexicon size of several hundred animals (Shrestha et al, 2015).

Semantic fluency is a widely applied, short duration test that uses commonly known targets and does not require special equipment to administer it. Diverse measures can be derived from semantic fluency testing; the most common metric is the number of unique items that are named. For animal naming, for example, repeated identical items are not double counted. However, different forms of the same taxonomic species, such as calf, cow, and bull, are usually counted as separate items. Similarly, hierarchical relationships are usually discounted, such that bird and eagle are considered to be separate items. Some studies have also considered mythical animals (unicorn) as valid responses. More sophisticated measures, such as clustering of similar taxonomic species or animals sharing similar habitats, have led to considerations of clustering and switching between subcategories (Troyer et al, 1998).

Graph Theory, Networks, and Network Analysis

Networks, also known as graphs, are used to model many types of relations and processes and are ubiquitous in biological, social, and physical systems. Graph theory is the study of a network, as they are mathematical structures that are used to model pairwise relations between objects (Albert and Barabási, 2002; Jeong et al, 2000). A network is constructed of nodes (also called vertices), which are connected by edges, symbolizing that the two nodes share a given feature. Network analysis is the process of deriving the graph theory attributes of a given network at the nodal, edge, and complete network level, leading to our understanding the structure of the network and allowing comparison between networks.

There are many methods that are used to construct graphs, even of the same system, depending on the relationships between two given nodes that allow an edge to be created between them. Network analysis computes attributes at the nodal, edge, and network level. Commonly measured attributes are the total number of nodes and edges, node degree (the number of edges attached to a given node), and the shortest path length between any two nodes (resulting in measures of mean node degree and mean shortest path length of the network). The clustering coefficient is a measure of how many nodes sharing an edge to node 1 are also attached to each other. Clustering is essentially a measure of triangles; in social networks, clustering occurs when two of my friends are friends with each other.

Real-world networks almost universally have several salient features known as scale-free networks and small-world properties. The concept of scale-free networks has been analyzed by Barabási and colleagues (Albert and Barabási, 2002; Jeong et al, 2000). Scale-free networks have two major features compared to a random graph.

• Network growth characterized by the “preferential attachment” of new nodes, resulting in a small number of “hubs” with large node degrees. A familiar example is the Internet, where a few sites such as Google or Yahoo have millions of linked pages, whereas vast numbers of sites have very few linked pages to or from them. An ancient version of this concept is the familiar epithet of “the rich get richer,” or the Matthew effect.

• Scale-free networks exhibit a power distribution such that plotting the node degree (the number of edges attached to a given node) versus the probability of having that node degree on a log-log scale results in a straight line (Albert and Barabási, 2002).

The small-world property was described by Milgram (1967), who observed that it often took only a few connections to send a letter across the country to someone who was personally unknown by the initial sender. The same concept has been popularized as the so-called 6 degrees of separation. The small-world property arises when most of your connections, such as your friends in a social network, are local, but a smaller number of your connections are distant, who in turn have a similarly structured social network. The small-world property of a network is characterized as having short path lengths and relatively high clustering. Brain connectivity manifests all of these features, which helps maximize connectivity in the constrained space available for the cerebral contents.

Graph Theory and Semantic Fluency

Several published methods of graph construction and analysis have been applied to semantic fluency graphs that have been constructed across groups of respondents, and their comparison is one of the main objectives of this study. In the case of the single individual, the results from a single individual’s semantic fluency tested once would be a simple chain of responses. Albeit interesting, the single chain lacks significant network properties: It has a clustering coefficient = 0 and a node degree = 2 for all but the first and last items, which would have a node degree = 1. The concept of mean path length in a chain is of unclear significance because it relates to position and not to the frequency of the item across a group of individuals (eg, dog and cat are more frequent than alligator or aardvark and usually have greater clustering coefficients and higher node degrees than less frequently named items). The interested reader is referred to Albert and Barabási (2002) for in-depth consideration of graph theory and network analysis and their applicability across all networks and -omics.

Bilingualism

Bilingualism is common throughout the world and uses final common pathways for word production after retrieval from semantic memory. Far from being a binary variable, bilingualism varies across the life span, reflecting an individual’s, age, social environment, and language usage patterns. It has been posited that bilinguals show an advantage in verbal tasks because they have increased executive functions necessary to switch between two languages.

Several studies have examined verbal fluency in bilinguals. Studying a heterogenous population of bilinguals, Luo et al (2010) found similar performance of monolinguals and bilinguals in semantic fluency but not letter fluency; the latter showed an advantage for bilinguals, especially those with “high” vocabulary skills. Friesen et al (2015) found that verbal fluency production was stable across adulthood, and the number of words produced in each language was affected more by age than by bilingualism in adults.

Paap et al (2019a, 2019b) investigated both a bilingual advantage and a bilingual disadvantage based on cross-language interference, treating bilingualism as a continuous variable based on self-rated verbal proficiency. Paap and colleagues (2019b) found no compelling evidence for a bilingual advantage in switching between groups or related words, comparing results from both letter and category fluency tasks, with monolinguals producing more animal names than bilinguals and letter fluency being similar across both language groups. In the latter study (Papp et al 2019b), differences in verbal fluency performance related to proficiency in the non-English language. These two studies included participants who were proficient in English and fluent in another language that was used daily without regard to the identity of the other language.

Rosselli et al (2002) studied English and Spanish monolinguals in English and Spanish on a lexical fluency (F-A-S) task and found no difference in the number of items they produced. In that study, English–Spanish bilinguals produced significantly fewer words than English monolinguals in the semantic fluency condition but not the phonological condition, which might be consistent with a bilingual deficit. Results in animal naming were similar in both languages across both monolinguals and bilinguals.

In a small study of semantic fluency in English–Spanish bilinguals (Salvatierra et al, 2007), normal older adults retrieved significantly more semantic items compared with phonemic items, whereas older adults with AD retrieved similar numbers of both types of items, suggesting greater decline in semantic fluency tasks for the AD group, as has been seen in many studies on individuals with mild cognitive impairment and those with AD.

Study Aims

The main aim of our study was to compare three analytical methods for constructing semantic fluency networks based on the semantic fluency testing of a convenience cohort of bilingual English–Russian participants. One important question is whether the underlying neural processes that are involved in semantic category fluency testing yield substantially different networks in different languages. The analytical methods we chose were originally published in different cohorts but converge in that they all use graph theory methods to produce metrics that are common to the final networks and are described in the Method section.

A secondary aim of our study was a conventional analysis comparing English and Russian responses on semantic fluency measures such as total number of items recorded and whether testing the first language affects production in the second language test. Demonstrating the practicality of using appropriate graph theory measures will allow for increased understanding of the complex network relationships that are encoded in the verbal fluency responses across the selected target population.

METHOD

Participants

We recruited study participants from the Russian community in Cleveland, Ohio, via word of mouth and local advertising at a Jewish community center. Inclusion criteria was age >18 years and self-rating as a Russian–English bilingual. Exclusion criteria was a diagnosis of dementia.

The study protocol was approved by the institutional review board of the University Hospitals Cleveland Medical Center and was performed according to the ethical guidelines of the Declaration of Helsinki and its later amendments. All individuals provided informed written consent before enrolling in the study.

Assessments

The second author (F.L.) tested each participant in person in their home during the day in a single visit lasting ~60 minutes. The visit included completion of a demographic form, category fluency testing in the first language (randomized), completion of the English version of the Montreal Cognitive Assessment (Nasreddine et al, 2005), and category fluency testing in the second language. The demographic form included information about where the individual was born, the age when English was first learned, and an estimate of the percentage of each language spoken per 10-year life interval. The percentages for each life interval were converted to a lifetime Russian index (100% English spoken). The index was derived by converting the estimated percentage of each language spoken over each 10-year interval into the percentage total area under the curve over the life span. For example, if a 60-year-old had learned English at age 10 years, and the percentage of Russian spoken from age 0–10 years was 100%; from age 10–20 years was 90%; 20–30 years, 50%; 30–40 years, 50%; 40–50 years, 10%; and 50–60 years, 10%, then the lifetime Russian index would be the sum of the percentages (ie, 310) divided by 600 (total possible), or 51.6%.

Upon completion of the demographic form, each participant then completed a 60-second animal naming task, randomized to either Russian or English tested first. Next, each participant completed the English version of the Montreal Cognitive Assessment, followed by the 60-second animal naming task in the other language. We chose to use the English version of the Montreal Cognitive Assessment because all of the participants were currently residing in the United States, and our main clinical and research testing is performed in English. All visits were audio-recorded, and animal names and timings were transcribed by two independent raters as previously described in Lenio et al (2016).

Definitions and Data Procedures

The total number of animals (N₆₀) represents the number of words that are produced by an individual, with obvious variants of the same term combined (man and human) but different forms of the same taxonomic species retained (cow and calf). In contrast to the procedure for counting the total number of unique items generated, duplicates were not deleted for purposes of network construction and analysis.

Graph Construction Methods

Simple Association

Lerner et al (2009) presented an initial approach to using graph theory to analyze semantic fluency in a study of older adults with normal cognition, those with mild cognitive impairment, and those with mild AD. In that study, all of the sequential chains of animals that were named were aggregated together, and unique sequences were extracted. Thus, if three individuals gave the following results—(a) cat, dog, and elephant; (b) cat, dog, elephant, and horse; and (c) dog, elephant, and moose—the resultant graph would have 5 nodes (ie, cat, dog, elephant, horse, moose) and 6 undirected edges (ie, cat–dog, dog–elephant, dog–horse, horse–elephant, cat–elephant, and elephant–moose). The highest node degree is elephant, with 4 edges connecting it to other nodes. The average path length for elephant is 1.0 because it is 1 edge distance from every other node. The average path length for horse is 1.5 (ie, [1 + 1 + 2 + 2]/4) (Figure 1).

FIGURE 1.

Example of network construction. If three individuals give the results of (a) cat, dog, and elephant; (b) cat, dog, elephant, and horse; and (c) dog, elephant, and moose, the resultant graph would have 5 nodes and 6 undirected edges of cat-dog, dog-elephant, dog-horse, horse-elephant, cat-elephant, and elephant-moose. The highest node degree is elephant, with 4 edges connecting it to other nodes. The average path length for elephant is 1.0 because it is 1 edge distance from every other node. The average path length for horse is 1.5 (ie, [1 + 1 + 2 + 2)/4). Adapted with permission from Lerner et al (2009).

To simplify edge construction, Lerner and colleagues (2009) considered each unique sequential pairing edge as a single connection no matter how many times it occurred, which is known as an unweighted edge. The authors also ignored the order in which the sequential pairings were produced, thereby creating an undirected network, so that elephant–whale was equivalent to whale–elephant. In Figure 1 (from 2009), the edges were dog–cat, cat–owl, owl–mouse, mouse–whale, whale–dolphin, dog–whale, whale–elephant, cat–goose, and goose–cow.

The results from that initial study (Lerner et al, 2009) showed that the number of nodes decreased from normal to mild cognitive impairment to AD, as did the edges, and measures of complexity such as clustering coefficient and mean shortest path length also changed consistently between the groups. Further analysis using this method of graph construction showed that this method produced scale-free networks with small-world properties, thereby providing validation for the methodology (Lenio et al, 2016; Lerner et al, 2009; Shrestha et al, 2015).

Corrected Associations/Conceptual

Goñi et al (2011) studied 236 Spanish individuals and introduced a statistical method that corrected for words that were produced consecutively beyond chance. The authors entered the matrices of words that each individual produced into the suite of MATLAB programs. This method makes statistical corrections for edges based on being beyond chance occurrence and the size of the window (ie, distance between animal names up to a distance of two links). Besides looking at direct neighbors connected beyond chance, the algorithm is also optimized to look at neighbors of neighbors. This method creates what the authors call a cognitive network, which is analyzed by using the graph theory methods incorporated here.

Goñi and colleagues (2011) also introduced the concept of an extended cognitive network, which adds in links based on modularity. Modularity is a concept that involves computing and plotting the generalized topological overlap measure (Yip and Horvath, 2007), an example of which is shown in Figure 2. Networks can be partitioned into modules, giving insight into the organization of a system and the basis of its structure, which is one of the major current topics of interest in the field of network theory (Danon et al, 2007; Yip and Horvath 2007). The generalized topological overlap measure (Yip and Horvath 2007) is a generalization or extension of the topological overlap measure (Ravasz et al, 2002) based on the selection of higher order neighborhoods.

FIGURE 2.

Generalized topological overlap measure plots.

The derived cognitive network and extended cognitive network are calculated by language and by using different statistical cutoffs for inclusion ($\text{α}$ = 0.05 and 0.25), as shown in Figure 3. The rationale for this approach is based on the observation that the participant group was relatively small (N = 51). The small size limited the number of items that were neighbors beyond chance when strict statistical significance cutoffs were used, which limited the utility of this methodology in comparison with the first method described earlier when applied to a much larger sample of semantic fluency results (Goñi et al, 2011).

FIGURE 3.

Cognitive network and extended cognitive network by language using different statistical cutoffs for inclusion ($\text{α}$ = 0.05 and 0.25 [Goñi et al, 2011]).

Network Community Approach

A third approach to network construction extended this network community concept further by constructing what the authors called a planar maximally filtered graph (PMFG; Kenettt et al, 2011, 2013; Tumminello et al, 2005). Network studies of verbal fluency using this approach have compared children with normal hearing to those with cochlear implants, and separately, semantic networks derived from the Hebrew associative word lexicon (Kenettt et al, 2011, 2013).

In this form of graph construction, one starts with all the collective data in a complete association correlation network for N target words containing N (N – 1) edges. Because most of the edges have small values (ie, weak correlations), the relevant information about the network (eg, topology, organization) can be obscured. Several statistical methods have been developed to overcome this obstacle by constructing from the complete network a subgraph that captures the most relevant information embedded in the original network. Engaging in data reduction to retain only the strongest correlations of co-occurrence in an individual’s verbal fluency results is to create a subgraph called the PMFG. Extracting this subgraph relies on hierarchical clustering, and the resulting subgraphs include all of the N nodes in the network whose edges represent the most relevant association correlations.

The basic steps of constructing the PMFG involve construction of a word correlation matrix. Computationally, the N (N – 1) values of the correlation matrix C are ordered in decreasing rank. We then start from the pairs of nodes with the highest correlation, say i and j, and draw a link between them. The process continues according to rank order, where in each iteration, a link is added if and only if the resulting graph (network) is still planar (ie, it can be drawn on the surface of a sphere without link crossing). In the final subgraph, the original values of the correlations are not retained (ie, all of the links have a weight of 1; it is unweighted, similar to the associative method described earlier).

Visualization and Network Analysis

We employed each of the methods for graph construction from semantic fluency testing and compared them with each other. We compiled a separate network graph for each language and computed each network’ properties.

We used the Cytoscape 3.7 visualization program to generate all of the network graphs (Shannon et al, 2003). We analyzed the data using the Cytoscape embedded plugins, Network Randomizer and NetworkAnalyzer, a program for graph analysis (Assenov et al, 2008). Graphs were also compared to random Erdos-Renyi networks of equal node number and equal number of edges and were evaluated for their scale-free and small-world properties (Erdös and Renyi, 1960). The graphs were also compared to a Watts-Strogatz lattice model for consideration of small-world properties (Bassett and Bullmore, 2006; Sporns and Zwi, 2004; Watts and Strogatz, 1998). JMP-14 (SAS) was used for statistical analysis.

RESULTS

Participants

Of the 57 participants we recruited, 51 met the inclusion criteria. Six participants were excluded because they were multilingual. The mean age of the participants was 49 (SD = 17.8), and the mean level of education was 4.1 (SD = 0.8) on a 1–5 scale, with 1 signifying lack of high school completion and 5 signifying completion of postgraduate studies. Of the participant pool, 73% were female. The demographics of the study population are provided in Table 1.

TABLE 1.

Study Participants’ Demographics (N = 51)

Measure	M (SD)
Age (years)	49.4 (17.8)
Level of education†	4.1 (0.8)
Gender (% female)	73
Age moved to United States (years)‡	32.0 16.0)
Age started second language (years)§	20.5 (17.0)
MoCA (30 points maximum)	21.4 (4.8)
MoCA Letter Fluency N words	11.1 (4.4)
N responses in English (N = 60)	16.1 (6.9)
N responses in Russian (N = 60)	18.4 (6.2)
Lifetime English Index (0–1)	0.21 (0.16)
Lifetime Russian Index (0–1)	0.76 (0.19)
Previous year English Index (0–1)	0.50 (0.27)
Previous year Russian Index (0–1)	0.49 (0.22)

^†Rating of 1–5: 1 = lack of high school completion; 5 = completion of postgraduate studies.

^‡Two participants were born in the United States.

^§The second language was English in all cases.

MoCA = Montreal Cognitive Assessment.

Overall, the participants produced significantly more words in Russian than in English (18.4 ± 6.2 vs 16.1 ± 6.9). There were no significant differences in total word production between the participants who were tested initially in English and those who were tested initially in Russian (ANOVA) (Table 2).

TABLE 2.

Characteristics of Word Production by Language and the Lack of Priming Effects Based on the First Language Tested for Verbal Fluency Output

	n	Words Produced M (SD)	Statistic
Language
Russian	51	18.4 (6.2)	t = 16.75, P < 0.0001
English	51	16.1 (6.9)
Russian responses
First trial Russian	24	17.8 (6.1)	F = 0.31, P NS
First trial English	27	18.8 (6.4)
English responses
First trial Russian	27	16.5 (7.7)	F = 0.12, P NS
First trial English	24	15.9 (6.2)

NS = not significant.

Table 3 shows the network measures that were derived from use of the entire sample using each of the network construction approaches described earlier. The table also shows the small-world properties of the networks in both languages, noting a smaller sigma value in Russian in some but not all of the constructed networks. Sigma is a scaled measure of overall small worldness for a given network (Sporns and Zwi, 2004). Because we are dealing with single values for each network, further analysis is qualitative rather than quantitative, as discussed in the following paragraphs. The overall differences shown in Table 3 do not show any consistent pattern that would suggest major differences between the two languages.

TABLE 3.

Network Measures by Statistical Method in Russian and English

Variable	Simple Association		Conceptual Network ($\alpha$ = 0.05)		Conceptual Network ($\alpha$ = 0.25)		PMFG
	Russian	English	Russian	English	Russian	English	Russian	English
n nodes	146	144	10	35	65	57	124	116
K (edges)	662	579	9	38	201	139	435	411
CC	0.188	0.206	0.0	0.09	0.61	0.52	0.49	0.49
Mean number of neighbors <k>	7.863	7.208	2.18	2.17	6.19	4.87	7.01	7.086
L (network)	2.888	3.017	2.38	5.96	3.38	3.36	3.43	3.388
Network diameter	7	7	4	15	7	8	8	8
Centralization	0.18	0.18	0.44	0.09	0.126	0.113	0.092	0.114
Slope of power law	−0.735	−0.815	N/A	−0.769	−0.263	−0.528	−0.783	−0.701
Erdos-Renyi simulation
P = <k>/N = CC (random)	0.054	0.05	0	0.062	0.095	0.086	0.057	0.061
L(random) = Ln N/[Ln(2K/N) – 1]	2.546	2.387	†	22.47	2.537	2.987	2.69	2.36
Lambda = L(net)/L(random)	1.185	1.210	†	0.265	1.333	1.126	1.277	1.287
Gamma = CC (net)/CC (random)	4.115	3.491	0	1.467	6.411	6.078	8.668	8.021
Sigma = Gamma/Lambda	2.885	3.473	0	5.528	4.81	5.40	6.79	6.23
Watts-Strogatz model
L lattice	9.566		—		5.84	5.18	8.20	7.69
CC lattice	0.643		—		0.6	0.6	0.642	0.643
Gamma scaled	0.228		—		1.02	0.84	0.74	0.737
Lambda scaled	0.069		—		0.255	0.17	0.135	0.149

CC = clustering coefficient. L = average path length over all shortest distances between any two nodes. PMFG = planar maximally filtered graph.

^†The calculated path length was negative. No further analysis is possible with this network.

The conceptual networks derived from the method of Goñi and colleagues (2011) were much smaller than the networks that were constructed from either the simple association method or the PMFG method, when $\text{α}$ = 0.05. Relaxing this criterion to an $\text{α}$ = 0.25 resulted in larger networks, with both scale-free and small-world properties.

Figure 3 show clustergrams that we constructed for networks with the PMFG methodology in each of the languages to show examples of community modularity in the data.

Comparison Between Languages

We randomly chose which language to test first, and there did not appear to be a significant priming effect. The number of words produced in Russian was significantly larger than the number produced in English, but the absolute difference of means was small (Table 3).

DISCUSSION

A very large amount of information is encoded in category fluency tasks, and many statistical aspects of semantic fluency remain under active study. Our study had two major objectives: (a) to test semantic fluency and to construct networks of participant responses in order to allow comparison of the results based on three different methods of network construction, and (b) to include observations related to differences between the languages using both conventional analysis and graph theory measures. Although the underlying data are identical, the statistical processing involved in each measure produces graphs of different node number and edge number. Therefore, any meaningful comparison needs to consider the properties that are derived from graph theory and to compare both between methods of network construction and between languages.

Comparisons Between Methods of Network Construction

The conceptual networks derived from the method of Goñi and colleagues (2011) produced much smaller networks at $\text{α}$ = 0.05 compared with the other methods. This finding is due to the stringent statistical correction for neighbors in the recall chain occurring beyond chance. Our cohort was much smaller than that of Goñi and colleagues’ (2011), and the overall number of words produced by our cohort was much smaller as well. Therefore, both the conceptual network and the extended conceptual network are similarly reduced compared with the findings of Goñi and colleagues (2011). We could calculate the networks based on a higher alpha, but the associations would not be statistically significant, which seems to defeat the purpose of setting rigid statistical significance in an exploratory analysis. Indeed, the Russian network under these conditions had a clustering coefficient = 0 and did not fulfill the criteria for a small-world network. Similarly, the ability to calculate the slope of the power law was very limited. Interestingly, there is little overlap in node identity between the two languages. The functional significance of these qualitative differences is unclear but may reflect cultural experiences in early childhood development.

The comparison of the simple association method and the PMFG method showed substantially bigger networks with both scale-free and small-world properties. One difference is the value of sigma, which is larger in Russian in the PMFG method and smaller in the simple association method. This qualitative difference does not suggest that there are major differences between languages nor that there are systematic changes such as forgetting of Russian evident in the results.

Overall, the results of these methods add robustness to the concept that semantic space is not fundamentally different in different languages. From a neurobiological standpoint, the storage and recall of semantic information uses final common pathway neural structures, again suggesting that these findings are unsurprising. The results also suggest that any of these methods would be adequate as a basis for using graph theory to analyze networks that are created from semantic fluency results, but the method of Goñi and colleagues (2011) is more dependent on large sample sizes.

Comparison Between Languages

Although not a primary feature of this study, our results allow for comparison of semantic fluency testing between languages, which is more akin to conventional analysis of the number of words that are produced over the conventional 60-second test duration.

We were concerned about priming effects induced by essentially asking for category fluency tests in different languages in close temporal proximity. We chose to randomize the order of the category fluency task rather than to simply divide the groups in advance, but there was no statistical difference in the number of named animals demonstrated between those tested first in English versus those tested first in Russian.

The recruited cohort consisted almost entirely of individuals who were born in the former Soviet Union. One concern might be that diminished use of the first learned language might lead to gradual forgetting of that language. In a previous study (Lerner et al, 2009), individuals with AD recalled fewer words and had scaled small-worldness measures (sigma) compared with individuals with mild cognitive impairment or normal cognition. In this study, we also found smaller sigma in Russian than English. However, there is no reason to believe that our findings are indicative of Russian being “forgotten.” The use of both languages was almost exactly equal within the year before testing, and the mean number of words produced per individual was higher in Russian, whereas the number of total animals named was essentially equal, and other graph measures were very similar between the two languages.

Clinical Implications

The findings presented here may be of use to a cognitive scientist or neurologist in several ways. The results could be expanded in planning future studies in defined niche populations that may be available to a researcher. Issues of sample size we encountered are also important for the cognitive scientist because network properties evolve with increasing sample size. It is important to recognize the contribution of different statistical techniques in understanding brain function in healthy and diseased models. Better understanding of how these variables interact awaits large collaborative and comparative studies.

Study Limitations

There are several limitations to this study. The study was not an epidemiological study, and the sample size was relatively small. It is well known that graph theory measures are dependent on the size of the cohort tested, and validation in a larger sample would shed light on this.

Network growth starts with an isolated node with no edges, but a critical juncture occurs with the emergence of scale-free properties (Albert and Barabási, 2002). It is clear from our previous work and the results presented here that group size is an important variable. Using subsets from a study of ~350 individuals, Shrestha et al (2015) modeled network growth and demonstrated the emergence and change of network parameters with group size. Although our cohort was relatively small, comparisons with Shrestha and colleagues (2015) indicate that network parameters are relatively stable and that our group size appears acceptable for the initial analysis presented here.

The use of a single bilingual group (Russian–English) is an advantage of this study, but the addition of monolingual controls in both languages would add to the results. We focused on a specific subset of bilinguals, as mixed bilingual populations (eg, English–Hindi and English–German individuals) might also present significant confounding of results. The inclusion of monolingual controls might have made the analysis significantly more complex without necessarily answering questions of bilingual advantage definitively. If there were significantly different network metrics in bilinguals versus monolinguals, it is possible that one might infer the presence or absence of a bilingual advantage.

CONCLUSION

The comparison of different analytical techniques reflects the growth of interest in networks in general, and an optimal graph theory analytical approach has not been defined and remains unstandardized between studies. Our study is one of the few to critically compare graph construction methods using a common data set. Comparison with other -omics-driven results in different subject groups would also be of interest going forward.

Glossary

AD

Alzheimer disease

PMFG

planar maximally filtered graph