Online Network Formation Among Students During COVID-19: Analysing Path Dependency in a Natural Experimental Setting

Abstract

The onset of COVID-19 in 2020 led to the closure of educational institutions and a shift to online teaching in India. It provides a natural experiment setting in which to examine the formation of endogenous ties among students and analyses the path-dependent nature of such a process. Information on sources of academic assistance was collected from members of two groups of students enrolled in the postgraduate course of the Economics Department of an Indian University using Google forms. The information was analysed using standard measures employed in social network analysis, such as sociograms, centrality measures, and homophily index. We show that, contrary to expectations, inheriting ties can constrain actors from forming ties that optimize outcomes.

JEL Classifications: D85, I20

Keywords

COVID-19 natural experiment network formation path dependency social network analysis India

1. Introduction

The impact of network structures on outcomes has been widely examined in different domains. Examples of such studies are diffusion of technology (Conley & Udry, 2010), job searches (Granoveter, 1994), criminal behaviour (Baerveldt et al., 2008), migration (Garip, 2008), occupational mobility (Munshi, 2011), worker’s productivity (Moretti, 2004), energy consumption (Ayres et al., 2013) and so on. Now networks are often formed endogenously, with actors choosing their peers. Studies have shown that preferential attachment to peers, vis-à-vis random formation of ties, enables agents to form ties with actors having high centrality positions (Topirceanu et al., 2018) and inherit centrality positions (Biggs & Shah, 2006; Gagnon & Goyal, 2017; Joshi et al., 2020). Preferential attachment, therefore, improves outcomes (Jackson & Rogers, 2007). Understanding how networks form and the role of preferential attachments in the formation of networks, therefore, becomes an important research question (Conley & Udry, 2010).

There has been a large body of theoretical work on the formation of networks—like Jackson and Wolinsky (1996), Bala and Goyal (2000), Dutta and Jackson (2003), Jackson (2010) and Joshi et al. (2020)—focussing on questions like how and why networks form, and the stability and efficiency of networks. In contrast, empirical studies of the process by which links are developed are rare. One reason may be that researchers are generally confronted with a pre-existing network that has taken a long time to form (and which persists even after the study is completed). Networks between students offer an opportunity to observe how links are developed. Ties start developing when students enrol in a programme, evolve over the duration of course and decay after the course is completed. Existing studies, however, focus on ties that are formed exogenously in a quasi-experimental setting through randomly assigned peers (Jain & Kapoor, 2015; Jain & Langer, 2019; Sacerdote, 2001; Zimmerman, 2003) or use existing data sets, such as the Wisconsin Longitudinal Study of Social and Psychological Factors in Aspiration and Attainment (Zax & Rees, 2002), AddHealth (Bifulco et al., 2011; Patacchini et al., 2017) and National Child Development Study (Patacchini & Zenou, 2012). A quasi-experimental design is based on randomly assigned links without giving actors the opportunity to choose peers. Although the ties in studies using large-scale data sets are formed endogenously, the pre-existing nature of ties in such data sets implies that it is not possible to examine how peers are chosen.

This study examines the formation of online ties among students enrolled in the Master’s programme of an Indian university. The sudden onset of COVID-19 and the closure of educational institutions in March 2020 enabled us to observe the formation of ties between students who were forced to shift to an online platform to form ties. Two groups of students are studied. While one group had inherited a network structure formed through face-to-face interaction in the pre-COVID period, the other group was admitted to the institute during the pandemic and did not have any such history. We are, therefore, able to study the selection of peers in real time in a natural experimental setting. Moreover, the differences in the background of the two networks enable us to examine how history in the form of past ties affects network formation and its outcome.

The paper starts with a review of the existing literature on the relationship between networks and academic performance; this discussion lays the ground for identifying the research question and hypotheses of this study (Section 2). The section goes on to describe the data collection and methods employed to analyse the data. Section 3 presents the findings. It is followed by a discussion of the results (Section 4). A concluding section (Section 5) summarizes the findings discusses its implications and identifies shortcomings and possible extensions of the study.

2. Materials and Methods

2.1 Review of Literature

In recent years, social network analysis has become also an important tool for analysing student networks (Saqr et al., 2018). Such studies have reported that a higher level of sociality improves learning outcomes (Cho et al., 2007; Patacchini et al., 2017; Richmond et al., 1987; Sacerdote, 2001; Saqr et al., 2018; Zirkin & Sumler, 1995), particularly if the actor enjoys a central position in the network (Brass & Burkhardt, 1993; Calvó-armengol et al., 2009; Cho et al., 2007; Sparrowe et al., 2001). This has also been confirmed by studies for Indian students (Jain & Kapoor, 2015; Jain & Langer, 2019). Weaker students are also reported to have benefitted from networks (Jain & Kapoor, 2015). Such effects are influential in the short run. In the long run, their influence depends upon the strength of ties; only ties that have continued over a long period have durable effects on educational performance (Patacchini et al., 2017).

However, these studies have been undertaken in the pre-COVID-19 period. The pandemic has posed several challenges to students. As the pedagogy process shifted to an online mode, students often faced problems related to interruptions in the power supply, weak or non-existent internet connectivity and high costs of acquiring the gadgets necessary for engaging in digital learning (Li et al., 2020). Online classes also limit interaction between faculty members and students. The absence of non-verbal, para-verbal and other social cues present in a face-to-face environment (Doran et al., 2011) implies that students cannot fully establish a cognitive social presence and affective social presence (Wut & Xu, 2021). It reduces the enthusiasm and concentration of the latter (Debbarma & Durai, 2021). Circulating study materials via online platforms such as e-mails, meetings over Zoom, YouTube and WhatsApp frequently lead to difficulties in understanding and promoted rote learning. As a result, the academic performance of students in fully online environments has not improved significantly compared to students experiencing face-to-face learning (El Said, 2021).

Further, students are fully confined to their homes, limiting all forms of face-to-face interaction. Social media provides the only form of social and academic interaction between students. Given that some studies have reported a weaker sense of community, sparser interaction and the exercise of selectivity in choosing whom to have ties within the relevant community (Lee & Bonk, 2016), it is important to assess the formation of networks within students who are forced by circumstances to engage in solely online interaction, understand the nature of such interactions and examine the impact of such interaction on learning outcomes. In this context, social network analysis is useful as it ‘provides a new paradigm and methods for assessing knowledge building in online learning communities’ (Wang & Li, 2007, p. 1).

2.2 Research Objective Questions and Hypotheses

The study examines the formation of ties between postgraduate students engaged in online learning during COVID in a Postgraduate Department of an Indian University. Two networks are compared. While one network was formed through online interaction only, the other was a ‘hybrid’ network formed by a combination of offline and online interactions. The paper argues that path dependency, or preferential attachment, is an important factor in the formation and efficiency of networks. Studies have shown that preferential attachment to peers with high centrality positions (Topirceanu et al., 2018), vis-à-vis random formation of ties, enables actors to inherit high centrality positions (Biggs & Shah, 2006; Gagnon & Goyal, 2017; Joshi et al., 2020) and improves outcomes (Jackson & Rogers, 2007). As the networks were formed for academic interaction, the natural outcome will be the Semester Grade Point Average (SGPA) secured in the semester for which interactions are studied. The hypotheses of our study may be stated as follows:

H ₁ : The duration and history of previous interactions will determine the nature of networks.

H _1a : If actors have a short period to form ties, they will form few but strategic ties with central actors. Such a network will be less dense but have a smaller diameter compared to a network derived between actors with a history of interactions.

H _1b : If actors are interacting for the first time, they need some basis to select potential peers. Given that some actors have a common past (they were undergraduates in Presidency University), subgroups will be formed on the basis of undergraduate college rather than other possible attributes like gender and caste. So the new network is hypothesized to exhibit ‘college-based’ homophily. As actors become familiar, other attributes may become important and form the basis for preferential attachment.

H ₂ : SGPA will be positively related to network position of actors.

H ₃ : The interactions between actors in the inherited network in the earlier semesters should have enabled them to identify suitable peers and form ties with them to maximize their benefits from the network. So the PG3 network should have better outcomes.

2.3 Data Collection

Data were collected from all students of the first and third semester enrolled in the Masters of Applied Economics course at the Economics Department of Presidency University (erstwhile Presidency College). They are referred to as PG1 and PG3, respectively. The former (PG1) was admitted in November–December 2020 when the University was closed because of COVID-19–related restrictions. As a result, this batch did not have any history of past interactions between themselves unless they were from the same undergraduate college. In contrast, the PG3 batch, admitted in July 2019, had been attending offline classes from August 2019 until mid-March 2020. So the network formed by PG3 students was a network structured by past offline interaction patterns. The onset of the pandemic sets up a natural experimental setting which enables us to examine the path-dependent nature of network formation.

The data were collected using Google forms, where the students were asked to report their names, gender, caste, their undergraduate college, (either from Presidency University, or elsewhere) and the names of their classmates whom they approached for academic help. The SGPA of each student was provided by the university authorities. The number of students is 43 (21 in PG1 and 22 in PG3). The low sample size implies that our study is of an exploratory nature and should be generalized with caution. But there are advantages of the small size—it enables us to capture the entire network data and analyse its formation without the confounding influence of external factors.¹

The sample profile is reported in Table 1. Female students comprise the majority in both networks (52.38% and 59.09% in PG1 and PG3 networks, respectively). In both classes, most of the students had completed their undergraduate course from outside Presidency University (61.9% in PG1 and 63.64% in PG3). There are 47.62% and 81.82% forward caste students in PG1 and PG3, respectively.² The mean SGPA of PG1 and PG3 students is 7.12 and 7.07. The median is also slightly higher among PG1 students (7.20, vis-à-vis 6.90). However, t tests for differences in mean and Kruskal–Wallis tests for differences in median do not indicate statistically significant differences in learning outcomes between the two groups.³

Table 1.

Sample Profile by Network.

Attributes	PG1	PG3	Total
Gender (%)
Female	52.38	59.09	55.81
Male	47.62	40.91	44.19
Undergraduate college (%)
Presidency	38.1	36.36	37.21
Others	61.9	63.64	62.79
Caste (%)
General caste	47.62	81.82	65.12
Others	52.38	18.18	34.88
SGPA
Mean SGPA	7.12	7.07	7.10
95% confidence limits	(6.64–7.61)	(6.75–7.39)	(6.81–7.38)
Median SGPA	7.20	6.90	7.00

Source: Estimated from data.

2.4 Methodology

2.4.1 Comparing Network Formation

To verify the hypothesis linking path dependency and the nature of networks, we will compare the basic characteristics of the two networks studied. We will start by analysing sociograms to identify underlying patterns. Following the visual analysis, we will estimate basic statistics relating to the two networks. Size (number of nodes), degree (number of links between actors) and density (the proportion of ties that have materialized out of all possible ties) are basic features of networks. To capture how the actors are embedded in the networks, we estimate the average distance between the actors. The most commonly used definition of distance between two actors is called the geodesic distance—the shortest distance between two actors. The longest path is called the diameter of the network. Generally, actors tend to interact with only a small proportion of others, many of whom know each other, i.e. form ‘clusters’. Clustering in a graph can be measured by examining the local neighbourhood (actors directly connected to ego) and calculating the density of this neighbourhood excluding the ego. Similarly, we can estimate it for all the actors, and find out the degree of clustering as an average of all neighbourhoods in the graph.

Another important feature of networks is the proportion of links of actors with the members of the same group (i.e. members having the same attribute). A social situation where the actors prefer to interact with the members of the same group, which the actor belongs to is known as homophily (McPherson et al., 2001). Krackhardt and Stern (1988) developed a measure of homophily using the E-I (external–internal) index:

E-I Index = T_{E} - T_{I} / T_{E} + T_{I}

(1)

when T_E is the number of external ties, and T_I is the number of internal ties. The E-I value ranges from −1 to +1. Values close to +1 indicate heterophily (i.e. actors prefer to interact with members outside their group); while a value of −1 indicates homophily. Values close to zero imply that ties are formed randomly.⁴

Another important characteristic of networks is its structure. This refers to the density of connections built up from dyads and triads. Network analysts argue that lines of cleavage and division may exist creating weak sub-components within the social fabric, that are less connected to the whole network. N-cliques are used to identify such structures. An n-clique is said to exist if every member of the clique is connected to the other actors by a geodesic distance of at most n. Generally, n = 2, so that all other members of a clique are either the friend of the ego or friend’s friend.

2.4.2 Econometric Model

To assess the impact of the network position of an actor on learning outcomes (H₂) we regress the following model:

Y = α + β_{1} NETWORK + β_{2} NETWORK 3 + β_{3} GENDER + β_{4} {UG}_{-} XYZ + ε

(2)

where

Y: SGPA in Odd Semester 2020

NETWORK: A measure reflecting position of the respondent in the network (captured by centrality measures, such as degree centrality, eigenvector centrality, closeness, betweenness and beta centrality)

NETWORK3: Network dummy = 1 if the student is a member of the PG3 network, and 0 otherwise

GENDER: Gender dummy = 1 if the student is male, and 0 otherwise

UG_Presidency: Undergraduate college dummy = 1 if student pursued undergraduate course from Presidency, and 0 otherwise

We will use centrality measures to capture the position of the actor in the network, and the E-I index to capture the extent of self-selection in the formation of ties. The following centrality measures are used:

Degree centrality: Degree centrality is the measure of an actor’s level of involvement in an activity. It measures the number of ties an actor has.

Eigenvector centrality: Eigenvector centrality considers the entire network. With eigenvector centrality, we consider the local network of actors immediately adjacent to the focal actor (Bonacich, 1987, 2007; Bonacich & Lloyd, 2001). It measures the number of direct ties of the ego to each alter, weighted by the degree centrality of the latter.

Betweenness centrality: Betweenness counts how many times an actor is placed on the geodesic path between the pair of actors (Freeman, 1978; Freeman et al., 1991). In networks studying information flows, betweenness helps to identify actors with high potential control over the diffusion of information (Cook et al., 1983).

Closeness: Closeness is measured as a distance between two actors. It emphasizes the actor’s independence.

The regression equation (2) is estimated for each of the centrality measures.

A potential problem with this model is endogeneity due to unobserved intellectual ability and academic motivation of respondents. However, the semester, gender and undergraduate dummies are unlikely to be correlated with intellectual ability. Similarly, the network variables are determined by personal traits (for instance, whether the actor is an extrovert has a pleasant personality and is helpful). It may be plausibly argued that such characteristics are unlikely to be correlated with intellectual ability. Discussion with students also indicated the absence of such correlation. Although we do not expect omitted variable bias, we have undertaken the Ramsay RESET test that further confirms the absence of omitted variable bias.

Self-selection in choosing peers may also lead to endogeneity (Bramoullé et al., 2009; Manski, 1993; Patacchini et al., 2017). In network terms, actors will exhibit homophily (McPherson et al., 2001) and tend to interact with participants sharing similar attributes. To address this issue we estimate the regression equation using the instrument variable method. We construct the instrument vector as the product of the normalized adjacency matrix and centrality measures. The instrument can be interpreted as the average centrality measures of the alters of an actor. As post-estimation exercises, we have checked for endogeneity using the Hausman test and assessed the strength of the instrument.

3. Results

3.1 Network Maps

Sociograms (Figures 1 and 2) are used to depict the information flow between actors in the network. The direction of an arrow between two actors, say from an actor A to another actor B, indicates that actor A seeks assistance/information from actor B.

Figure 1 gives the network map for the ties between the PG1 students. The map reveals that there is a greater connection (direct and indirect ties) between the actors. Even the actors at the periphery of the network (such as PG23, PG24, PG28, PG30, PG34, PG35 and PG37) are well connected since they have ties with the focal players (PG22 and PG39) and have at least two peers. We can see that the actors are close to each other; it should be reflected in terms of shorter geodesic distance and diameter. Key players (PG22 and PG39) can be easily identified in the network. They are the class representatives who are selected by the students. Their centrality scores are high (see Supplementary Table S1), indicating strong connectivity with other students. Actors who were Presidency undergraduates are coded in green. Although there is one cluster present in the north-west periphery of the network, other Presidency undergraduates are scattered throughout the network.

The map in Figure 2 depicts the ties that exist between the PG3 students. The network map for PG3 shows that actors are more scattered compared to PG1. Although PG44, PG46 and PG53 appear to have a greater number of ties with the other actors in the network, it is not easy to identify key players. The class representative (PG50) is not a key player; in fact, he is at the periphery of the network. The peripheral player PG58 has only one peer, which is with a non-focal actor (PG60). Similarly, PG62 has only two direct ties, though one of them is with a focal node (PG46). The green-coded actors (Presidency undergraduates) are clustered in the north-west periphery of the network.

It is possible that subgroups existing within a larger network may be denser than the overall network; it is referred to as modularity (Sinha, 2014). Since undergraduate students of Presidency University had a long history of interaction starting in 2016 (for PG3 students; 2017 for PG1 students), they may initially be expected to have strong ties and interact more with themselves rather than with ‘strangers’. The subgraph for such students, drawn in Figure 3, does not display any modularity for the PG3 students. While the subgraph for PG1 reveals one cluster, two mutually exclusive clusters are observed for the PG3 students. It indicates that, in the PG3 network, even the undergraduate students of the university did not have close ties with each other.

3.2 Attributes of Networks

The characteristics of the two networks are given in Table 2. The two networks are of almost the same size, with 21 (PG1) and 22 (PG3) nodes. It implies that they are comparable. The potential number of directed ties for PG1 and PG3 are 441 and 462, respectively. The proportion of ties that have actually materialized (density) is low in both networks. Among PG1 students only 17% of potential ties (74 ties) have materialized; the corresponding percentage among PG3 students is 19% (88 ties). Average degree, a statistical measure that indicates on average how many actors does an actor have links/ties with, is also lower in the PG1 network, as compared to that of PG3. This is expected given the differences in duration of the interaction.

Table 2.

Basic Features of the Networks.

Measures	PG1	PG3
# of nodes	21	22
# of possible ties	441	462
# of ties that have materialized	74	88
Density	0.17	0.19
Average degree	3.52	4.00
Proportion of ties within 3	0.78	0.67
Geodesic distance	2.00	2.69
Diameter	4	6
Weighted overall graph clustering coefficient	0.24	0.27

Notes: Average degree represents the average number of ties/links each actor has with other nodes.

Source: Estimated from data.

Even though the number of ties among PG1 students is lower than among PG3 students, the reachability level is higher in the former group. The proportion of ties within 3 is higher in PG1 (78%) compared to PG3 (67%). It indicates that four out of five actors of the PG1 network are either a friend or a friend’s friend; in the PG3 network, it is much lower. Both the geodesic distance and diameter (largest geodesic in the network) is lower in the PG1 compared to the PG3 network. Reachability and compactness are thus higher in the PG1 vis-à-vis the PG3 network—particularly if we consider the fact that PG1 actors had interacted for a shorter period of interaction. It implies that the quality of the PG1 network is better than that of the PG3 network as diffusion of information within the PG1 network is likely to be faster and more pervasive despite a lower density. The clustering coefficient gives an idea about the degree to which the nodes tend to cluster in the network. The weighted overall graph clustering coefficient is higher for PG3 compared to PG1. Networks that are more clustered may be expected to have a higher number of cliques and exhibit homophily. As we will see in the next subsection, this is exactly what occurs. Overall, we find that although the hybrid PG3 network is denser it has a larger diameter compared to the virtually formed PG1 network formed through interaction over a shorter period. The reason is that PG1 actors formed links with four actors (including the two class representatives). As a result, density (proportion of potential ties that materialized) was low, but reachability between actors was (through the four key actors) high. The latter reduces distance, validating the first sub-hypothesis (H₁a).

3.3 Homophily and n-Cliques

We have taken the gender of the students, caste and their undergraduate college (i.e. either from Presidency University or elsewhere) as possible attributes for forming groups. Results indicate the presence of gender and college-based homophily (Table 3).⁵ The E-I index measuring college-based homophily is negative and statistically different from zero, indicating the presence of homophily in both networks. It is surprisingly higher among PG3 students (−0.31) compared to PG1 students (−0.19). The results also reveal the presence of gender-based homophily only among PG1 students, particularly among female students.⁶

Table 3.

E-I Index for PG1 and PG3 Students.

GROUP	PG1		PG3
GROUP	UG non-Presidency	UG Presidency	UG non-Presidency	UG Presidency
Internal ties	46	24	76	12
External ties	24	24	23	23
E-I index	–0.314	0.000	–0.535	0.034
Actual value	–0.186		–0.313
Expected value	–0.010		–0.091
Std. dev.	0.118		0.109
Probability	0.074		0.032
	Female	Male	Female Students	Male
Internal ties	56	24	16	44
External ties	27	27	29	29
E-I index	–0.349	0.059	0.289	–0.205
Actual value	–0.194		–0.017
Expected value	0.013		0.048
Std. dev.	0.087		0.103
Probability	0.034		0.287

Note: (1) Direction of ties is ignored. (2) The top panel reports values for groups formed on the basis of undergraduate college, while the bottom panel report results for gender-based groups.

Source: Estimated from data.

The reason for the persistence of college-based homophily until the third semester is surprising. We would normally expect students from other colleges to be accepted and integrated over time. The reason why it did not occur for PG3 actors lies in the personality of the students graduating from Presidency University. While one group of students were introverts (PG47, PG49, PG50 and PG57), another group displayed a snobbish attitude and kept to themselves (PG61 and PG62). The presence of homophily implies divisions within the network structure. Analysis of n-clique results confirms the existence of subgroups in both networks. The PG1 network, however, has fewer cliques than the PG3 network (4 versus 9 cliques) as undergraduate college was the only basis for forming groups. Moreover, considerable overlap exists between the cliques formed in the PG1 network, with the class representatives (PG22 and PG39) playing a major role in linking the cliques (Figure 4). Analysis of the PG3 network reveals considerable fissures, leading to distance between the cliques. A possible reason, revealed in discussion with the students, is the inherited nature of the network, and the role of personal factors that influenced the choice of peers in the earlier semesters. It results in the PG1 network having a stronger and more inclusive structure compared to the PG3 network. The nature of the subgraph possibly reflects the personalized nature of ties in the PG3 network.

Overall, group closure is observed in both networks. The basis of within-group interaction, however, differs between the two networks. Among PG1 students, who do not have any past interaction and have never met face to face, both gender-based⁷ and college-based homophily is observed. On the other hand, actors in the PG3 network tend to interact based on whether they had completed their undergraduate course in Presidency University. The results imply that actors in both networks do not choose alters randomly but exercise selection. However, the subdivisions produced by homophily in the PG1 network produce fewer and overlapping subgroups. It results in a tighter structure, with connections existing between the groups, facilitating information flow throughout the entire network. The results support the second sub-hypothesis (H_1b) also.

3.4 Centrality Measures

Degree centrality measures the immediate contacts an actor has in a network. The mean gives the average centrality measure for all the students. Table 4 reveals that mean degree centrality and betweenness are higher in the PG3 network vis-à-vis the PG1 network, although the differences are statistically insignificant at the 10% level. The value of the eigenvector centrality is also the same in both batches. Closeness, however, is significantly higher in the PG1 network vis-à-vis in the PG3 network, providing more evidence in support of the hypothesis that peers in the PG1 network will be closer vis-à-vis those in the PG3 network (H_1a).

Table 4.

Centrality Measures in the PG1 and PG3 Networks.

PG1 Network	Degree Centrality	Betweenness	Closeness	Eigenvector Centrality
Mean	5.62	4.09	59.26	0.20
Std dev	4.24	8.724	10.11	0.09
Sum	118	85.79	1,244.52	4.14
Variance	17.95	76.10	102.22	0.01
Minimum	0	0	51.28	0.08
Maximum	15	30.452	90.91	0.45
PG3 Network	Degree Centrality	Betweenness	Closeness	Eigenvector Centrality
Mean	6.09	7.71	54.53	0.20
Std dev	2.58	7.68	7.01	0.09
Sum	134.00	169.52	1,199.58	4.30
Variance	6.63	58.93	49.18	0.01
Minimum	2.00	0.00	39.62	0.05
Maximum	13.00	26.71	70.00	0.38
Network differences
t-statistic	–0.19	–1.41	1.75*	–0.02

Source: Estimated from data.

Note: * denotes Prob < 0.10.

3.5 Networks and Learning Outcomes

We next estimate equation (2) using the centrality measure of alters as an instrument. Results are reported in Table 5. The t-statistic of the coefficient for the instrument in the first-stage model indicates a close association between the instrument and the endogenous variable. This is confirmed by the F-statistic from the first stage; it shows that all the instruments are relevant except for the E-I index.⁸ Testing for exogeneity of the instrument is not easy. The values of the correlation with SGPA are low,⁹ but it does not take into account the effect of the instrument after incorporating the control variables.¹⁰

Endogeneity was found for only the models capturing network position using eigenvector centrality (χ² = 3.36 and 4.26, significant at the 10% level); the results of the two-stage least-square models, however, revealed β₂ to be statistically insignificant even at the 10% level (see Supplementary Table S3). These models are not reported for the sake of brevity. In case of betweenness, closeness and the E-I index, the ordinary least-square model is appropriate (χ² = 0.62, 2.65 and 0.24). The results of these models are reported in Table 5.

The coefficients of the betweenness and closeness measures are positive and statistically significant. It implies that being in a strong position in the network is associated with high grades. A ‘between actor’ is in an advantageous position because that actor has control over the flow of information. Such students are gatekeepers in the process of information diffusion between other actors. Since (s)he is the intermediary through which the information flows, (s)he gets access to a large proportion of the information flowing in the network. Closeness i.e. proximity to peers may help in securing information through spillovers. Interestingly, the class representatives in PG1 had higher closeness and betweenness scores compared to other actors, but they did not perform well academically.¹¹ The class representative in PG3 had become a peripheral actor during the pandemic possibly because he was focussing on completing internships; his performance was also not satisfactory.

Table 5 also reveals that the coefficient of the E-I index is positive and significant at the 10% level. A higher proportion of contacts with actors outside one’s endogenously formed group benefits students. The observed tendency of both networks to interact within endogenously formed groups is a weakness of both networks and constrains the ability of actors to utilize networks to improve learning outcomes. Our findings, therefore, validates hypothesis 2 (viz. that network position affects learning outcome) partially.

Table 5.

Regression Output of Learning Outcomes on Network Measures.

Variables	Betweenness	Closeness	E-I Index
Network measure	0.21**	0.16*	0.46*
GENDER	–0.08	–0.16	-
Presidency	1.07***	1.08***	-
Network3	–0.12	0.04	-0.03
Intercept	6.66***	5.73***	7.25
N	43	43	43
F	7.82**	7.54**	1.9
R ²	0.33	0.31	0.06
Ramsay reset: F	0.32	0.37	0.75

Source: Estimated from data.

Notes: (1) * P < 0.1; ** P < 0.05; *** P < 0.01. (2) In case of network measures, standardized coefficients are reported.

Table 5 reveals that actors with high betweenness and closeness scores are better placed to attain high grades. It implies that if actors of a particular network have higher betweenness or closeness scores, the network is more efficient in terms of securing grades for its members. Now, the kernel density of these scores reveals that betweenness scores are similar between the two networks, while members of the PG1 network have higher closeness scores (Figure 5).¹² Results show that PG1 actors have significantly higher closeness scores than PG3 actors. Since closeness is positively related to grades (Table 5), this places the PG1 network in a more advantageous position vis-à-vis the PG3 network. The results, somewhat unexpectedly, reject our hypothesis that the inherited network would secure better outcomes (H3).¹³ A possible reason is strategic tie formation in the PG1 network. Faced with a time constraint, PG1 students preferred to form ties with the class representatives and other key actors (PG30 and PG33), enabling them to maximize the academic benefits from the network. In contrast, the PG3 network was inherited from the pre-COVID period, and ties were formed based on personal relations. It was not optimized for facilitating information flows.

4. Discussion

The two networks studied differ with respect to the duration of interaction (PG1 actors had less than four months) and the platform of interaction (hybrid vis-à-vis online). In the case of offline interaction, potential friends can be observed and visual cues obtained from his/her behaviour. Further, PG3 students reported, initial contacts occur publicly when both actors are part of a group; they (particularly female students) felt safety in numbers. In the virtual world, on the other hand, the cost of investing in building up the ties is higher compared to that in the physical world because of technological reasons.¹⁴ It is not surprising, therefore, that the density and average degree of ties are slightly higher in the PG3 network as they had greater time to interact among themselves and had a more favourable platform to assess possible peers based on personal compatibility for the purpose of social interaction. The ties preceding the online network created a fragmented network characterized by non-overlapping subgroups. Given that relations had already been formed for social interaction, it was not easy to restructure ties for facilitating information dissemination by discarding former peers and establishing fresh links with students with whom interaction had been restricted. Consequently, information diffusion was not pervasive but restricted within cliques. When the shift to online interaction occurred, therefore, the inherited ties became a constraint. Instead of being a ‘silver spoon’ (Joshi et al., 2020), the inherited network became a baggage.

Given the technological and temporal constraints on their interaction, on the other hand, PG1 students responded by behaving strategically—forming indirect ties, overlapping cliques and reducing the distance between actors, thereby shortening the diameter of the network. The absence of a history of interactions, faceless interaction, personal compatibility—which are normally constraints to social interaction—became features on which the PG1 students thrived. As personal compatibility issues were minimized, actors were able to form ‘close’ ties if it facilitated information flows. As seen earlier, the average closeness score of the PG1 network was significantly higher than that of PG3. Closeness, a measure of the distance between two actors, indicates an actor’s ability to access information in the network (Leavitt, 1951). If an actor is close to other actors, then (s)he can have access to information without any intermediaries. This resulted in faster dissemination of information between PG1 actors. Even though self-selection divided the networks into subgroups, the sub-components were overlapping and had ties with each other. The class representatives, in particular, played a major role as brokers in bridging structural holes in the network. The PG1 network became, therefore, a more inclusive network, characterized by fast and pervasive information flow. This confirms results reported in existing studies that efficient networks will form when strategic individuals choose to add or delete links based on only localized pay-offs (Vallam et al., 2014).

5. Conclusion

Our study examines the formation of two student networks through online interactions during COVID-19. Actors in one network had previous offline interactions, so that they inherited pre-existing ties. The other group was without any inherited links. These differences were exogenous and created a natural experiment setting to study the path-dependent nature of network formation and the resultant impact of peer effects on grades. Our results show that the existence of links preceding the formation of a network offers actors opportunities but also imposes constraints as the purpose of forming the original network may not be the same as the subsequent network. If existing peers do not have the characteristics necessary to attain the desired outcomes, establishing fresh ties is required. However, given past patterns of interaction, it may be costly to realign and form ties with students whom an actor had previously avoided. The PG1 students, on the other hand, were constrained by the short interval before their examinations started, and self-selected to form ties that would facilitate information diffusion. Given the small sample size, however, our study is exploratory in nature, which limits generalization of the results. It highlights the importance of studying how past ties can shape interactions in the present and affect the outcomes of forming a network.

Footnotes

Acknowledgements

We are grateful to the comments and suggestions made by Sudipta Sarangi, Virginia Polytechnic Institute and State University that helped to focus the paper and sharpen the analysis. The detailed comments and suggestions made by the anonymous reviewers are also acknowledged. All remaining errors and omissions are the responsibility of the authors.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Notes

ORCID iD

Zakir Husain

Supplemental Material

References

Ayres

, Raseman

, & Shih

(2013). Evidence from two large field experiments that peer comparison feedback can reduce residential energy usage. Journal of Law, Economics, and Organization , 29(5), 992–1022.

Baerveldt

, Völker

, & Van Rossem

(2008). Revisiting selection and influence: An inquiry into the friendship networks of high school students and their association with delinquency. Canadian Journal of Criminology and Criminal Justice , 50(5), 559–587.

Bala

, & Goyal

(2000). A noncooperative model of network formation. Econometrica , 68(5), 1181–1229.

Bifulco

, Fletcher

J. M.

, & Ross

S. L.

(2011). The effect of classmate characteristics on post-secondary outcomes: Evidence from the add health. American Economic Journal: Economic Policy , 3(1), 25–53.

Biggs

, & Shah

M. K.

(2006). African SMES, networks, and manufacturing performance. Journal of Banking & Finance , 30(11), 3043–3066.

Bonacich

(1987). Power and centrality: A family of measures. American Journal of Sociology , 92(5), 1170–1182.

Bonacich

(2007). Some unique properties of eigenvector centrality. Social Networks , 29(4), 555–564.

Bonacich

, & Lloyd

(2001). Eigenvector-like measures of centrality for asymmetric relations. Social Networks , 23(3), 191–201.

Bramoullé

, Djebbari

, & Fortin

(2009). Identification of peer effects through social networks. Journal of Econometrics , 150(1), 41–55.

10.

Brass

D. J.

, & Burkhardt

M. E.

(1993). Potential power and power use: An investigation of structure and behavior. Academy of Management Journal , 36(3), 441–470.

11.

Calvó-armengol

, Patacchini

, & Zenou

(2009). Peer effects and social networks in education. Review of Economic Studies , 76(4), 1239–1267.

12.

Cameron

A. C.

, & Trivedi

P. K.

(2005). Microeconometrics: Methods and applications . Cambridge University Press.

13.

Cho

, Gay

, Davidson

, & Ingraffea

(2007). Social networks, communication styles, and learning performance in a CSCL community. Computers & Education , 49(2), 309–329.

14.

Conley

T. G.

, & Udry

C. R.

(2010). Learning about a new technology: Pineapple in Ghana. American Economic Review , 100(1), 35–69.

15.

Cook

F. L.

, Tyler

T. R.

, Goetz

E. G.

, Gordon

M. T.

, Protess

, Leff

D. R.

, & Molotch

H. L.

(1983). Media and agenda setting: Effects on the public, interest group leaders, policy makers, and policy. Public Opinion Quarterly , 47(1), 16.

16.

Debbarma

, & Durai

(2021). Children and youth services review educational disruption : Impact of COVID-19 on students from the Northeast states of India. Children and Youth Services Review , 120(November 2020), 105769. https://doi.org/10.1016/j.childyouth.2020.105769

17.

Doran

P. R.

, Doran

, & Mazur

(2011). Social network analysis as a method for analyzing interaction in collaborative online learning environments. Journal of Systemics, Cybernetics and Informatics , 9(7), 10–16.

18.

Dutta

, & Jackson

M. O.

(2003). Networks and groups: Models of strategic formation . Springer.

19.

El Said

G. R.

(2021). How did the COVID-19 pandemic affect higher education learning experience? An empirical investigation of learners’ academic performance at a university in a developing country. Advances in Human-Computer Interaction , 2021(3), 1–10.

20.

Freeman

L. C.

(1978). Centrality in social networks conceptual clarification. Social Networks , 1(3), 215–239.

21.

Freeman

L. C.

, Borgatti

S. P.

, & White

D. R.

(1991). Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks , 13(2), 141–154.

22.

Gagnon

, & Goyal

(2017). Networks, markets, and inequality. American Economic Review , 107(1), 1–30.

23.

Garip

(2008). Social capital and migration: How do similar resources lead to divergent outcomes? Demography , 45(3), 591–617.

24.

Granoveter

(1994). Getting a job: A study of contacts and careers . Northwestern University Press.

25.

Jackson

M. O.

(2010). Social and economic networks . Princeton University Press.

26.

Jackson

M. O.

, & Rogers

B. W.

(2007). Meeting strangers and friends of friends: How random are social networks? American Economic Review , 97(3), 890–915.

27.

Jackson

M. O.

, & Wolinsky

(1996). A strategic model of social and economic networks. Journal of Economic Theory , 71(1), 44–74.

28.

Jain

, & Kapoor

(2015). The impact of study groups and roommates on academic performance. Review of Economics and Statistics , 97(1), 44–54.

29.

Jain

, & Langer

(2019). Does whom you know matter? Unraveling the influence of peers’ network attributes on academic performance. Economic Inquiry , 57(1), 141–161.

30.

Joshi

, Mahmud

A. S.

, & Sarangi

(2020). Network formation with multigraphs and strategic complementarities. Journal of Economic Theory , 188(6), 105033.

31.

Krackhardt

, & Stern

R. N.

(1988). Informal networks and organizational crises: An experimental simulation. Social Psychology Quarterly , 51(2), 123.

32.

Leavitt

H. J.

(1951). Some effects of certain communication patterns on group performance. The Journal of Abnormal and Social Psychology , 46(1), 38–50.

33.

Lee

, & Bonk

C. J.

(2016). Internet and higher education social network analysis of peer relationships and online interactions in a blended class using blogs. The Internet and Higher Education , 28, 35–44. https://doi.org/10.1016/j.iheduc.2015.09.001

34.

, Industries

, Forum

W. E.

, Lalani

, Curator

, Industries

, & Forum

W. E.

(2020). The COVID-19 pandemic has changed education forever. This is how . 2–7.

35.

Manski

C. F.

(1993). Identification of endogenous social effects: The reflection problem. The Review of Economic Studies , 60(3), 531–542.

36.

Maurya

R. K.

(2018). In their own voices: Experiences of Dalit students in higher education institutions. International Journal of Multicultural Education , 20(3), 17.

37.

McPherson

, Smith-Lovin

, & Cook

J. M.

(2001). Birds of a feather: Homophily in social networks. Annual Review of Sociology , 27(1), 415–444.

38.

Moretti

(2004). Workers’ education, spillovers, and productivity: Evidence from plant-level production functions. American Economic Review , 94(3), 656–690.

39.

Munshi

(2011). Strength in numbers: Networks as a solution to occupational traps. The Review of Economic Studies , 78(3), 1069–1101.

40.

Patacchini

, Rainone

, & Zenou

(2017). Heterogeneous peer effects in education. Journal of Economic Behavior & Organization , 134, 190–227.

41.

Patacchini

, & Zenou

(2012). Juvenile delinquency and conformism. Journal of Law, Economics, and Organization , 28(1), 1–31.

42.

Richmond

V. P.

, Gorham

J. S.

, & Mccroskey

J. C.

(1987). The relationship between selected immediacy behaviors and cognitive learning. Annals of the International Communication Association , 10(1), 574–590.

43.

Sacerdote

(2001). Peer effects with random assignment: Results for Dartmouth roommates. The Quarterly Journal of Economics , 116(2), 681–704.

44.

Saqr

, Fors

, Tedre

, & Nouri

(2018). How social network analysis can be used to monitor online collaborative learning and guide an informed intervention. PLOS ONE , 13(3), e0194777. https://doi.org/10.1371/journal.pone.0194777

45.

Sinha

(2014). The importance of community: How modular organization of social networks affects their collective dynamics. Studies in Microeconomics , 2(1), 49–61.

46.

Sparrowe

R. T.

, Liden

R. C.

, Wayne

S. J.

, & Kraimer

M. L.

(2001). Social networks and the performance of individuals and groups. Academy of Management Journal , 44(2), 316–325.

47.

Staiger

, & Stock

J. H.

(1997). Instrumental variables regression with weak instruments. Econometrica , 65(3), 557.

48.

Tierney

W. G.

, Sabharwal

N. S.

, & Malish

C. M.

(2019). Inequitable structures: Class and caste in Indian higher education. Qualitative Inquiry , 25(5), 471–481.

49.

Topirceanu

, Udrescu

, & Marculescu

(2018). Weighted betweenness preferential attachment: A new mechanism explaining social network formation and evolution. Scientific Reports , 8(1), 10871.

50.

Vallam

R. D.

, Subramanian

C. A.

, Narayanam

, Narahari

, & Srinath

(2014). Strategic network formation with localized pay-offs. Studies in Microeconomics , 2(1), 63–119.

51.

Wang

, & Li

(2007). Social network analysis of interaction in online learning communities. The 7th IEEE International Conference on Advanced Learning Technologies, ICALT 2007, ICALT , 699–700.

52.

Wut

, & Xu

(2021). Person-to-person interactions in online classroom settings under the impact of COVID-19: A social presence theory perspective. Asia Pacific Education Review , 22(3), 371–383.

53.

Zax

J. S.

, & Rees

D. I.

(2002). IQ, academic performance, environment, and earnings. Review of Economics and Statistics , 84(4), 600–616.

54.

Zimmerman

D. J.

(2003). Peer effects in academic outcomes: Evidence from a natural experiment. Review of Economics and Statistics , 85(1), 9–23.

55.

Zirkin

B. G.

, & Sumler

D. E.

(1995). Interactive or non-interactive? That is the question!!! The Journal of Distance Education/Revue de l’ducation Distance , 10(1), 95–112.

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