structural_complexity {CurricularAnalytics}

Calculate structural complexity

Description

A helper function for calculating the structural complexity for each node and the total structural complexity of a curriculum graph.

Usage

structural_complexity(node_list, edge_list)

Arguments

node_list

Dataframe with an 'id' column for each node and a 'term' column specifying which term the course is to be taken in.

edge_list

Dataframe with two columns 'from' and 'to' specifying directed edges starting at 'from' nodes directed towards 'to' nodes. Entries must use node ids from node_list.

Details

The structural complexity of a node v_k is defined as a linear combination of the node's delay and blocking factors. More formally

h(v_k) = d(v_k) + b(v_k)

. The structural complexity of an entire curriculum graph G_c is defined as

h(G_c)=d(G_c)+b(G_c)=\sum_{v_k \in V} \left(d_c(v_k) + b_c(v_k)\right)

Value

A list that contains the following:

bynode

A dataframe containing the structural complexity of each node

total

The total structural complexity of the curriculum graph

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
node_list <-
data.frame(
 id = 1:4,
 label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
 term = c(1, 1, 2, 2)
)
sc_list <- structural_complexity(node_list,edge_list)
print(sc_list)
# Output:
# $bynode
#   id sc
# 1  1  5
# 2  2  1
# 3  3  4
# 4  4  3
# $total
# [1] 13