Introduction
Background
Networks in physics education research
Networks of ideas
Student collaboration networks
Previous exam network studies
Data
Race/ethnicity | Count | Percent |
---|---|---|
American Indian or Alaska Native | 191 | 0.68 |
Asian | 806 | 2.85 |
Black or African American | 4497 | 15.90 |
Hispanic of Any Race | 1599 | 5.65 |
Native Hawaiian/Pacific Islander | 35 | 0.12 |
Non-Resident Alien | 245 | 0.87 |
Race and ethnicity unknown | 730 | 2.58 |
Two or more races | 782 | 2.76 |
White | 19,404 | 68.59 |
Total | 28,289 |
Total | Percent | |
---|---|---|
Undergraduate | ||
Male | 9599 | 41.66 |
Female | 13,440 | 58.34 |
Graduate | ||
Male | 1630 | 34.45 |
Female | 3101 | 65.55 |
Medical | ||
Male | 161 | 51.44 |
Female | 152 | 48.56 |
Dental | ||
Male | 103 | 50.00 |
Female | 103 | 50.00 |
Total male | 11,493 | 40.63 |
Total female | 16,796 | 59.37 |
Methods
Creating networks
Global statistics
Node property measures and distributions
igraph
package (Csardi and Nepusz 2006) to compute these centrality measures for our networks. While it is not generally expected for these measures to strongly correlate for a single network, we are interested in understanding how node centrality changes as the network develops. We will use the directed versions of betweenness and eigenvector centrality calculations, as they reflect the available information about reciprocity of ties, which has been found to segregate by grade over the semester (Wolf et al. 2017). We will also choose inward directed measures (in-degree and in-closeness) as each of these scores for a person do not depend on the relationships reported by that person. For example, my out-degree is simply how many people that I reported working with, while in-degree is the number of people who reported working with me.Network partitioning measures
edge-betweenness
algorithm for this purpose (Newman and Girvan 2004). Because the name edge-betweenness gives the reader insight as to the network properties whereby this algorithm makes communities, we will use that name for the rest of this paper. However, community detection algorithms don’t give us much insight into the social roles that individuals are playing within a network. For this, we will look at structural equivalence. Structural equivalence partitioning methods focus on how vertices connect to other vertices, and groups vertices if they share similar linking behavior. For example, the outer nodes of a star-shaped network would all be structurally equivalent to each other and thus form a block, even though none of them directly connect to each other. Structural equivalence algorithms are good at doing a positional or role analysis in social networks. We will use the CONCOR
algorithm (Breiger et al. 1975) for this purpose.Edge betweenness
cluster_edge_betweenness
function in the igraph
package (Csardi and Nepusz 2006) of the R programming language (R Core Team 2020). The only required input to this function is the network object, however it can be configured to treat a directed network as an undirected network or change the weights of edges. We used this algorithm in the default configuration, allowing it to account for the information embedded in the directional network ties.CONCOR
concorR
package (Suda et al. 2020).Network visualization
Longitudinal analysis
Results and discussion
Fall 2015
Global and node-level measures
Nedge | Reciprocity | Density | AvgDeg | Transitivity | AvgCC | AvgDist | AvgDistUC | Assort |
---|---|---|---|---|---|---|---|---|
223 | 0.83 | 0.12 | 10.14 | 0.83 | 0.30 | 2.03 | 33.35 | 0.46 |
172 | 0.63 | 0.09 | 7.82 | 0.54 | 0.35 | 4.34 | 16.65 | 0.03 |
211 | 0.78 | 0.11 | 9.59 | 0.81 | 0.30 | 2.04 | 33.89 | 0.32 |
247 | 0.75 | 0.13 | 11.23 | 0.79 | 0.33 | 4.25 | 11.33 | 0.53 |
399 | 0.84 | 0.21 | 18.14 | 0.61 | 0.22 | 2.31 | 2.31 | 0.19 |
Network partitioning
Spring 2016
Global and node-level measures
Nedge | Reciprocity | Density | AvgDeg | Transitivity | AvgCC | AvgDist | AvgDistUC | Assort |
---|---|---|---|---|---|---|---|---|
160 | 0.65 | 0.13 | 8.89 | 0.73 | 0.36 | 2.79 | 18.16 | 0.04 |
162 | 0.74 | 0.13 | 9.00 | 0.78 | 0.31 | 3.60 | 15.20 | 0.44 |
161 | 0.71 | 0.13 | 8.94 | 0.68 | 0.34 | 2.74 | 17.79 | 0.10 |
180 | 0.77 | 0.14 | 10.00 | 0.71 | 0.32 | 1.88 | 24.46 | 0.20 |
258 | 0.78 | 0.20 | 14.33 | 0.62 | 0.24 | 2.39 | 4.25 | 0.21 |