Heterogeneity, incomplete information and efficiency: a longitudinal study of a students’ network

doi:10.21203/rs.3.rs-2356403/v1

There is a considerable body of evidence showing that ties between actors are not random but are formed endogenously to maximise individual benefits. Such preferential attachment may be difficult if information is incomplete; in such cases, repeated interaction with the same set of agents may facilitate the identification of actors with whom forming ties is beneficial. The present study examines the formation of ties in a heterogeneous community characterised by incomplete information about the endowments of actors. Data was obtained through an online survey from students enrolled in the post-graduation programme in the department of Economics, Presidency University, and analysed using social network analysis tools and concepts. Results revealed that, over time, the density, reachability and connectivity of the network increased. Greater interaction among actors facilitated the identification of high value actors, and led to an efficient and stable network—but at the cost of polarisation within the network. The study concludes by arguing the need to supplement the analysis of efficiency and stability with an enquiry into the normative implications of polarisation.

JEL classification: D85, I29

Social Network Analysis

Information

Preferential attachment

Efficiency

Social network analysis refers to the study of interpersonal relationships. It is formally defined as a collection of nodes (actors) linked by several relationships indicated by uni-directional or bi-directional ties. Network structures have been widely examined to study ties between job market applicants (Granoveter, 1994; Granovetter, 1983), heart patients (Fowler & Christakis, 2009), terrorists (Krebs, 2002), migrants (Garip, 2008; Munshi, 2011), cyberbullies (Barlett et al., 2018), and telecommunication firms (Barnett, 2001), and so on. Now ties between heterogeneous actors may be formed randomly or endogenously. There has been extensive research on preferential attachment (Jackson, 2005; Jackson & Rogers, 2007), based on either attributes (Bourdieu, 1984, 1988; McPherson et al., 2001) or centrality positions in inherited networks (Joshi et al., 2020). The basis of tie formation and the resultant network structure will depend upon the context and the nature of incentives from exchange (Burger & Buskens, 2009; Jackson & Xing, 2014).

Now actors may differ from each other (Goldsmith-Pinkham & Imbens, 2013) so that their effects on outcomes will vary. When actors possess perfect information about peers, self-selection of peers is relatively easy (Bala & Goyal, 2000; Jackson & Xing, 2014; Johnson et al., 2009). Incomplete information about peers may, however, hinder the process of tie formation (Goeree et al., 2009). In such cases, repeated interaction may allow actors to obtain information about peers (Chen et al., 2014; Roth & Schoumaker, 1983). Studying such dynamic interaction is not easy and has been undertaken mainly in either networks with pre-existing or endogeneously formed ties. Practical difficulties have limited the study of the origin of networks and interaction till the cessation of interaction. The present study examines the patterns of tie formation and its evolution in a student network. The size of the network is constant over time, and interaction occurs over a period of three semesters. We show that ties are formed selectively, leading to the networks becoming more efficient over time. However, the increased efficiency comes at the cost of polarisation that may affect equity within the network.

The paper is structured as follows: Section 2 states the objective and hypotheses of this study; it is followed by a discussion of the data and method used in the study (Section 3). Section 4 presents the results, while the next two sections discuss the results and draws appropriate lessons from the study.

2.1 Literature review

In recent years, the role of social processes in the formation of the study has become a growing area of research (Leung, 2019). In their seminal study, Bala and Goyal (2000) have examined strategic tie formation in the presence of perfect information. It is an important area of research given the heterogeneity of actors (Goldsmith-Pinkham & Imbens, 2013). While some studies have shown that differences in productivity levels among actors may lead to homophily (Jackson & Xing, 2014; McPherson et al., 2001), the presence of differences in the endowment of actors may also facilitate exchange and encourage heterophily (Johnson et al., 2009; Kimura & Hayakawa, 2008; Rogers & Bhowmik, 1970). In general, however, imperfect information, asymmetric linking opportunities and the presence of existing ties among some actors may constrain preferential attachment optimising individual pay-offs (Goeree et al., 2009). Lacking information, actors joining a network may perform local searches in the neighbourhood of randomly met peers (Jackson & Rogers, 2007). Alternatively, actors may rely on other cues for selecting peers (Biggs et al., 2002; Biggs & Shah, 2006; Kossinets & Watts, 2009; C. Zhang et al., 2017); such focal play may lead to the evolution of cultures or conventions (Jackson & Xing, 2014; Schelling, 1960). A recent study reports that incomplete information may lead to the development of biased perceptions about potential peers, so that individual utility maximisation may lead to group segregation, reducing social welfare (Zhang & Carver, 2022). In dynamic games, however, repeated interaction enable agents to observe their potential peers over time and assess their productivity, trustworthiness and other relevant attributes; it enables actors to revise the assessment of which actors to form ties with (Chen et al., 2014; Roth & Schoumaker, 1983). Star networks may develop in such situations, based on a single high value agent, with the centrality, stability and efficiency of the network increasing over time (Goeree et al., 2009).

Existing studies on tie formation among heterogeneous actors with incomplete information are either based on a theoretical structure (Bala & Goyal, 2000; Dutta & Jackson, 2003; Jackson, 2010; Jackson & Wolinsky, 1996), or behaviour of agents in laboratory settings (Goeree et al., 2009). Empirical studies based on the actual behaviour of communities are rare, and mostly use either an endogenously formed network (Sacerdote, 2001), or large data sets containing information on existing ties (Chandrasekhar & Jackson, 2018; Jain & Kapoor, 2015; Jain & Langer, 2019; Patacchini et al., 2017). In contrast, longitudinal studies of the formation of networks are rare because of the practical difficulties of studying networks over the entire duration of interaction. Fresh entry and attrition are other constraints (Biggs et al., 2002; Greif, 1989; Kali, 1999).

2.2 Objective and hypothesis

The present study uses data collected from post graduate students in a single department of an Indian University to examine the evolution of ties formed for academic purposes over the first three semesters of the programme.[1] Studying student networks in non-residential academic institutions have some advantages. Given the short duration of the course, stability in network size, heterogeneity with respect to academic merit and availability of information about actors in initial stages of interaction,[2] the study of ties between students provide an opportunity to examine the interplay of heterogeneity and lack of information to examine the evolution of the network and its characteristics over time.

The present study argues that the absence of information about the productivity (in terms of academic merit) of each actor constrains optimal tie formation in the first semester.[3] Since there has to be some basis for choosing peers, ties will initially be formed on the basis of easily observed markers like the under graduate college (whether studied in Presidency, or not). In this phase, class representatives will be the key players in the network. Subsequently, actors gain information about each other and ties will form on the basis of academic performance in the previous semester. High value actors will emerge with high centrality scores; they will compete with, and even displace, the class representatives as the key players.[4] Simultaneously, given that academically strong students gain by interacting between themselves rather than with weaker students, polarisation is expected occur within the network. It will be reflected in increasing homophily.

The hypotheses of this study are:

1. Over time the density, centrality, compactness and connectivity of the network will increase (H1);

2. Ties will be formed selectively, leading to polarisation and the emergence of marks based homophily (H2);

3. The number of high value actors will increase over time (H3); and

4. The network will become more efficient and stable over time (H4).

2.3 Data

The data was collected from students enrolled in the Masters of Applied Economics course of the Economics Department of Presidency University, Kolkata, in 2020. The post-graduate programme comprises four semesters over a period of two years. The first semester normally starts in July and ends in December. However, in 2020, the course started in January 2021 as a result of the Covid-19 pandemic. The first two semesters had to be completed within the first six months due to the delay in the academic schedule (they ran from January to March, and April to July). The third semester commenced in mid-August and continued until January 2022.

The data was collected using Google forms, where the students were asked to report the names of their classmates whom they approached for academic help. Such data was collected after the end of each of the semesters to study the evolution of the network formed, and assess the corresponding changes in network positions for each of the actors. In addition, after informing the students information about their gender, caste, religion, their undergraduate college (that is, whether from Presidency University, or elsewhere), Semester Grade Point Average (SGPA) obtained was extracted from the records. Informed verbal consent of the students were taken and the data anonymised.

The number of students was 21. The majority of the students were females, Hindus, general social groups and had completed their undergraduate degree outside Presidency University (Table 1).

Table 1

Sample profile
Characteristics	Number	Percentage
Gender
Male	10	47.62
Female	11	52.38
Religion
Hindu	18	85.71
Muslim	3	14.29
Social category
General	11	52.38
Disadvantaged	10	47.62
Under Graduate College
Presidency University	8	38.10
Other universities	13	61.90
Source: Estimated from data

2.4 Methodology

This study uses standard measures like degree, density, reachability, distance and centrality to capture the main network characteristics.

The number of actors in the network is its size. Given a network of n actors, there are potentially n×(n-1) directed ties. The density of a network is the ratio of the actual number of ties to the potential number of ties. The average number of connections each node has with other nodes is the average degree of the network.

If reachability is high in a network, information will be transmitted throughout the network regardless of the point of its origin. An actor is reachable by another if we can trace a set of connections from the origin (i.e., the source) to the target actor, irrespective of the number of actors in between them. However, even if an actor might successfully communicate with another, the connection between them may be weak. By weak ties we mean that there are few pathways connecting two actors. In such cases, actors have a low connectivity, which means that there are few routes for information to travel from one actor to the next.

To capture the aspect of how the actors are embedded in the networks, a common approach generally employed is to examine the distance between the actors. If two actors are adjacent, then the distance between them is one. The distance among the actors is an important macro-characteristic of the network as a whole. The most commonly used definition of distance between two actors is called the geodesic distance; it is the shortest distance between two actors. The longest path is called eccentricity, with the largest eccentricity in the network being the diameter of the network.

While the centrality of an actor assesses the roles of each agent and identifies their importance in the network, the average centrality score of the network indicates whether the actors are becoming more powerful over time. Centrality is estimated using degree, betweenness and closeness. Degree centrality is a measure of an actor's level of involvement or activity in the network. Specifically, it measures the number of ties an actor has. In this case, we are measuring out-degree centrality which measures the number of alters an actor sought information from.

\({\text{C}}_{\text{D}}\left(\text{i}\right)\text{=} \sum _{\text{j}\text{=1}}^{\text{n}}{\text{x}}_{\text{ij}}\) [1]

When x_ij is the value of the tie from actor i to actor j (value is either 0 or 1) and n is the number of nodes in the network. Betweenness centrality deals with an actor’s position in the entire network. It counts how many times an actor is placed on the geodesic, which is the shortest path linking two actors (Cook et al., 1983; Freeman, 1978):

\({\text{C}}_{\text{B}}\left(\text{k}\right)\text{=} \sum \frac{{\text{∂}}_{\text{ikj}}}{{\text{∂}}_{\text{ij}}}\text{, }\text{i }\text{≠}\text{ }\text{j }\text{≠}\text{ }\text{k}\) [2]

where \({\text{∂}}_{\text{ikj}}\) is the number of geodesics linking actors i and j passing through the node k, and \({\text{∂}}_{\text{ij}}\) is the number of geodesics linking actors i and j. Closeness is another measure of centrality, which considers the entire network. It emphasises the actor's ability to access information in the network easily (Leavitt, 1951), power (Coleman, 1973) and influence (Friedkin, 1991). Here, closeness is measured as the distance between two actors:

\({\text{C}}_{\text{c}}\left(\text{i}\right)\text{=} \sum _{\text{j}\text{=1}}^{\text{n}}{\text{d}}_{\text{ij}}\) [3]

where d_ij = distance connecting actor i to actor j.

Substructures within the network are analysed using the clustering coefficient and E-I index. While the overall graph clustering coefficient is simply the average of the densities of the neighborhoods of all of the actors, the weighted version attaches a weight to the neighborhood densities proportional to their size (Watts, 1999).[5] The E-I index is used to measure the degree of homophily (Krackhardt & Stern, 1988). It is given by:

E-I index = \(\frac{{\text{T}}_{\text{E}}\text{-}{\text{T}}_{\text{I}}}{{\text{T}}_{\text{E}}\text{+}{\text{T}}_{\text{I}}}\)[4]

where, T_E = the number of external ties; T_I = the number of internal ties.

Sociograms—visual depictions of ties linking actors in a network—are used to examine the nature of ties formed, particularly whether a star formation develops. They also identify key players. In addition, the centrality scores of each actor and their scores as hubs and authorities (Kleinberg, 1999) are estimated. Authorities are actors who can directly provide information; on the other hand, hubs are actors who do not have the information themselves but can either direct other actors to the best source of information or provide the information after collecting the same from another actor.

The efficiency of the network was analysed using the average of the mean ranks of egos of every actor:

\(\sum _{\text{i=1}}^{\text{21}}\sum _{\text{j=1}}^{{\text{n}}_{\text{i}}}{\text{R}}_{\text{ij}}\) [5]

when R_ij is the rank of all the egos (j = 1, … n₁) for each actor i. A decline in the average rank over time implies that actors are choosing their peers more efficiently.

The stability of the network is examined using stability and expansion ratios. They are defined as follows:

Stability ratio = \(\frac{\text{Ties retained from previous semester}}{\text{Ties in previous semester}}\) [6]

Expansion ratio = \(\frac{\text{Ties newly formed in current semester}}{\text{Ties in previous semester}}\) [7]

Fragmentation is a measure that helps to identify how many nodes are not able to interact among themselves if a certain actor is removed from the network. The mean fragmentation score also indicates the stability of the network.

[1] In the fourth semester students undertook projects, which limited their interaction; so ties in the last semester were not studied.

[2] Some students had studied in the University for their Bachelors programme; such individuals have inherited ties between themselves. The network also comprises actors who are strangers to each other as they have joined the University from other institutes.

[3] The lack of information is compounded by the online nature of interaction in the first semester. The difficulties of forming ties in online student communities has been discussed in Namhata et al. (Namhata et al., 2022).

[4] The two class representatives were selected through a process of self-nomination, followed by voting by the students. Though not a rule, students were advised to select one representative from Under Graduate students of the University and another from new entrants to the institute.

[5] It implies that actors with larger neighborhoods get more weight in computing the average density.

3.1 Network measures

The network measures are reported in Table 2. The number of nodes was 21, implying a potential 420 ties between the actors. The number of ties, density and average degree of the network had increased consistently over the three semesters, indicating increasing interaction. The rising degree centrality indicated an increase in tie-formation between actors over the study period. The closeness measure was higher in Semester 3 compared to Semester 1; it implies faster dissipation of information in the network. Only betweenness centrality remained stable over the period of study. The network also became more compact and connected over time. The analysis, therefore, validates H1 (density, centrality, compactness and connectivity of the network will increase). Paradoxically, however, both the geodesic distance and the diameter had increased. Further, the proportion of actors within a distance less than three declined. It implies the possibility of clusters in the network.

Table 2

Network Measures
Measures	Sem1	Sem2	Sem3
Number of nodes	21	21	21
Number of ties	74	84	94
Average degree	3.52	4.00	4.48
Density	0.18	0.20	0.22
Reachability
Connectedness	0.78	0.91	0.91
Compactness	0.45	0.48	0.48
Fragmentation	0.22	0.10	0.10
Distance
Average geodesic distance	2.00	2.39	2.60
Proportion within three	0.78	0.76	0.71
Diameter	4.00	7.00	7.00
Centrality
Degree	0.28	0.32	0.35
Betweenness	0.40	0.40	0.40
Closeness	0.59	0.57	0.59
Clustering
Overall graph clustering coefficient	0.49	0.24	0.34
Weighted overall graph clustering coefficient	0.24	0.22	0.27
Source: Estimated from data

3.2 Clustering and homophily

The overall graph clustering coefficient displayed a U-shaped trend (Table 2). After weighing for network size, however, we found that clustering had increased from 0.24 (Semester 1) to 0.27 (Semester 3).

A relevant question in this context relates to the possible basis for the formation of clusters. Attributes like gender, caste and religion turned out to be statistically insignificant in all semesters and are not reported. The E-I Index for undergraduate college (Table 3) indicated the presence of homophily only in Semester 1 (-0.186). In the first semester, students coming from different colleges were strangers entering into an unfamiliar environment and needed time to choose their egos. This led them to cluster together. In contrast, students of Presidency University were situated in a familiar environment and had already formed ties with their peers. Over time, however, the actors interacted between themselves online and through social media (like Facebook) and started forming ties. In subsequent semesters, therefore, the E-I index became statistically insignificant.

To test for homophily based on academic performance, we calculated the median marks obtained by the students in the previous semester. In the case of semester 1, the final marks obtained in the University examinations were considered. Students were categorised into two groups— those who obtained marks above the median marks and those who secured marks below the median marks. Table 3 revealed the absence of a statistically significant level of marks-based homophily in semester 1 (E-I Index = 0.474). The undergraduate examination had been conducted on an online mode and the assessment process varied across institutions. So students reportedly felt that marks secured in the Under Graduate examination was not a reliable indicator of academic merit. In the second semester, when the assessment became uniform, the actors displayed marks-based homophily (-0.097), which increased further to (-0.135) in the third semester. The hypothesis that the observed index differs from zero was statistically significant at a ten and five per cent level, respectively. It implies selective attachment among actors and polarisation based on academic performance, confirming H2.

Table 3

E-I index over semesters
Statistics	Semester 1	Semester 2	Semester 3
Under Graduate college
Observed E-I index	-0.186	-0.094	-0.081
Expected E-I index	-0.01	-0.01	-0.01
Std. Dev.	0.116	0.108	0.096
Probability	0.074	0.274	0.263
Academic performance
Observed E-I index	-0.051	-0.125	-0.135
Expected E-I index	0.048	0.048	0.048
Std. Dev.	0.085	0.097	0.087
Probability	0.171	0.052	0.027
Source: Estimated from data

3.3 Sociogram

The sociograms depicting nature of interactions visually are given in Figs. 1, 2 and 3. In Fig. 1, we observe that the class representatives (PG22 and PG39) are two key players in the network. Connectivity appeared quite high. Even the actors at the periphery (PG28, PG37, PG35, PG21, PG27) were well connected and hade ties with the class representatives and with some other students.

Figure 2 indicates an increase in connectivity between actors. Compared to semester 1, the density of the network had increased. The number of key players had increased each other from two to four—in this semester the key actors include the class representatives (PG22 and PG39) and two new actors (PG20 and PG40). Both these students were students of Presidency University at the undergraduate level, and were in the academically superior group. Although there were fewer people at the periphery of the network, the connectivity of those at the periphery seems to have reduced. For instance, PG32, PG37 and PG36 had only two direct connections each.

Figure 3 depicts a greater density among the actors compared to Semesters 1 and 2. More key players had emerged, although the class representatives were still occupying an important position in the network.

3.4 Position of different actors

The analysis of centrality, hub and authority scores indicate the position of the actors (Appendix Tables A1 and A2). In the first semester, the class representatives (PG22 and PG39) were central actors, with high centrality, hub and authority scores. The authority score of PG22 was much higher than the hub score while it was the opposite in the case of PG39. In other words, while PG22 could provide information directly, PG39, on the other hand, could collect the information successfully and pass it on to other students. With the progression of the semesters, however, their importance in the network declined. It may be attributed to their poor academic performance. The class representatives were displaced by other students as key actors in the network. For instance, PG20 improved his centrality scores consistently over the semesters. The actor was chosen to be the placement coordinator of the batch at the end of the first semester and was also academically strong (among the top three students). PG20, PG30 and PG33 became authorities while PG20, PG34, PG38, and a few others became hubs by semester 3.

A plausible explanation of the changes is that the actors obtain more information about each other as they interact with each other. Starting from the second semester, they also obtain information about academic merit as grades are published. Students who performed better became more prominent. However, there was a non-linearity as students who performed best was not willing to share information with other students. For instance, PG31, who was the topper of the batch, did not interact with his peers. Actors, therefore, established connections with their peers who were close to the top and shared information. In the second and third semesters, placement and internship emerged as important issues. As a result, the importance of placement coordinators (PG20 and PG40) rose in these semesters as they provided information about the prospective companies and internship opportunities to their peers.

Thus, the pattern of tie-formation changed over time as actors obtained the information necessary to identify high value actors. The influence of academic performance and other academic accomplishments of actors become increasingly significant in determining their position in the network. This is validated by the analysis of the sociograms and ego-centric measures indicate that H3 (increase in the number of high value actors) holds. However, the network did not resemble the star formation. Rather, there are inter-connections between actors.

3.5 Stability and efficiency of network

Changes in the fragmentation scores (reported in Table 2; 0.22 in Semester 1, 0.10 subsequently) and the stability and expansion ratios (see Table 4) indicates that the network has become more stable over time. Since forming and maintaining ties was costly—once information was received about the helpfulness, academic strength and the nature of the different actors—the actors discarded old ties that yielded less benefit and developed bonds with relatively more high valued actors.

Table 4

Changes in ties over semesters
	Semester 1 & 2		Semester 2 & 3
Ego	Stability Ratio	Expansion ratio	Stability Ratio	Expansion ratio
PG20	0.500	2.000	0.600	0.200
PG21	1.000	0.000	1.000	0.000
PG22	0.889	0.222	0.600	0.000
PG23	0.500	1.500	0.500	0.250
PG24	1.000	0.250	0.600	0.000
PG25	0.500	0.000	0.333	1.000
PG26	0.500	1.000	1.000	0.500
PG27	0.000	2.000	0.750	0.500
PG28	0.000	0.000	0.750	0.500
PG29	1.000	1.667	1.000	0.250
PG30	1.000	0.250	0.600	0.000
PG31	0.500	0.000	1.000	1.000
PG32	0.167	0.167	0.500	1.500
PG33	0.400	0.200	1.000	0.667
PG34	0.333	0.333	0.000	1.000
PG35	0.500	1.000	0.667	0.667
PG36	0.000	1.000	1.000	0.500
PG37	1.000	0.000	1.000	0.500
PG38	1.000	5.000	0.833	0.167
PG39	0.417	0.167	1.000	0.286
PG40	0.500	0.000	0.000	3.000
Mean	0.557	0.798	0.702	0.595

Source: Estimated from data.

If we correlate the change in ties with academic performance in the previous semester, we find that students had tried to establish new ties with peers who had secured high grades, and discarded peers whose performance was below par. Such behaviour was reflected in the statistically significant decline in mean rank of peers between the first two semesters from 10.298 to 8.582 (Table 5). Subsequently, however, the change was marginal and statistically insignificant. Over time, therefore, the network became more stable and efficient (H4).

Table 5

Mean of ranks of peers in each semester
Statistic	Semester 1	Semester 2	Semester 3
Mean	10.298	8.582	8.847
t-statistic		1.518*	-0.207

Note: * denotes Prob. < .10.

Source: Estimated from data.

To sum up, the results of this study indicate increasing interaction among actors reflected in increases in average degree, density and reachability. Centrality scores (degree and closeness) also rises, though marginally. In the absence of information, actors initially form ties based on an easily observed indicators (undergraduate college) and consider the class representatives as high value actors. With increasing interaction, however, actors obtain greater information about their peers. It leads to the decline in the value of the class representatives, emergence of more high value actors and a shift towards marks-based homophily and polarisation. Consequently, the network became more efficient and stable. Thus, the four hypotheses framed are all validated.

Existing studies have reported that, though networks will become denser, more connected integrated (Barnett, 2001), their geodesic distance will increase over time (Spencer, 2003). Literature also reports that new entrants to a network cluster together (Bernard, 2013); however, the basis of tie formation changes over time (O’Malley & Christakis, 2011) and may lead to polarisation (Jackson & Xing, 2014; McPherson et al., 2001). These is also evidence that increasing interaction generates information and enables identification of high value actors (Chen et al., 2014; Roth & Schoumaker, 1983). It increases efficiency of the network (Barnett, 2001; Bottinelli et al., 2019; Long et al., 2016); along with the emergence of multiple high value actors the network, therefore, becomes more stable over time (Bowker, 2004; Dakin & Ryder, 2020). The present study confirms all these findings.

On the other hand, the findings of this study contradicts that of existing studies reporting increasing dependence on a few key value actors leading to a fragile (Malin & Carley, 2007) and less clustered network (Scribani et al., 2021). The results of the present study also differs from that of studies reporting that actors tend to form ties with known peers (Biggs et al., 2002; Biggs & Shah, 2006; Jackson & Rogers, 2007). Nor does this study observe the creation of star networks reported by Goeree et al. (2009).

This study highlights the importance of obtaining information through greater interaction in a community characterised by actors with varying and unknown levels of productivity. Results reveal that the network will become stable, efficient but polarised over time. This is an important finding which is becoming increasingly recognised in literature (Sih et al., 2009). It has implications beyond student communities and applies in contexts like group-based production, evolution of communities with unequal distribution of endowments, etc.

The small sample size is a major limitation of this study. As pointed out Leung (https://doi.org/10.1016/j.jeconom.2019.01.010), making inferences from the results is possible under very restrictive conditions. The present study is, therefore, exploratory and indicates a possibility that needs to be explored through studies using larger samples. However, the small sample size does enable the study of the complete network and all ties.

The present study examines the formation of ties among actors with unequal endowments and lacking information. Analysis reveals that lack of information in the initial stages of interaction need not constrain the movement towards efficiency. Repetitive interaction in a dynamic context may generate information and create stable and efficient ties between actors. This is an encouraging finding. However, the normative implications of these findings needs to be explored. The efficiency of the network is attained with a cost in the form of increasing polarisation among actors. Now, the raison-d’être of networks is the spill over of positive externalities within the community (Fowler & Christakis, 2009; Kincaid, 2000). The creation of a polarised society imposes barriers to the dissipation of externalities within the community. It calls for the creation of overlapping structures measures like mediation (Bartolomeo & Papa, 2016) and exogenous appointment of bridging players (Musiał & Juszczyszyn, 2009). A study of the possible conflict between efficiency and equity in heterogeneous networks comprises an important area of research for the future.

The authors have no competing interests to declare. The study did not receive any funding. Informed verbal consent was sought from all respondents.

ACKNOWLEDGMENT

Comments received by Diganta Mukherjee, Achin Chakrabarty and Sattwik Santra are gratefully acknowledged. All remaining errors and omissions remain the responsibility of the authors.

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No competing interests reported.

Appendix.docx

Heterogeneity, incomplete information and efficiency: a longitudinal study of a students’ network

Status:

Version 1

Abstract

Figures

1. Introduction

2. Materials And Methods

2.2 Objective and hypothesis

2.3 Data

2.4 Methodology

3. Findings

3.1 Network measures

3.2 Clustering and homophily

3.3 Sociogram

3.4 Position of different actors

3.5 Stability and efficiency of network

4. Discussion And Conclusion

Declarations

References

Additional Declarations

Supplementary Files

Status:

Version 1