Expanding Network Analysis Tools in Psychological Networks: Minimal Spanning Trees, Participation Coefficients, and Motif Analysis Applied to a Network of 26 Psychological Attributes

Table 4

An overview of the three methods.

MINIMUM SPANNING TREE
Recommended for network	Dense networks and/or networks with many small edges
Important procedure steps	(1) Selecting a distance measure: (i) Gower’s distance; (ii) Distance inversely proportional to the shared variance; (2) Centrality analysis (by inspection or/and with standard centrality measures computed)
Output	MST – the filtered network
Methodological considerations	Distance measures (i) and (ii) will produce different MSTs if a network has negative
Other analytical possibilities	Looking at MST branches as communities; Using MST to test the robustness of the network estimation of the most essential edges MST can include distance metric as weight for further analysis
Effect of reverse-coding variables	(i) affecte  (ii) not affected
Hypothesis/Research question	RQ: Which node is the most central?; Which (overlapping) communities exist in the network?
PARTICIPATION COEFFICIENT as a corrective
Recommended for network	(1) Pre-existing differences in the kinds of nodes; (2) Networks with communities
Important procedure steps	If (1) is true: (a) Defining the node groups; (b) Calculating PC; (c) Choosing the centrality measure to be corrected with PC (optional); If (2) is true: (a) Data-driven detection of communities; (b) Calculating PC; (c) Choosing the centrality measure to be corrected with PC; (d) Comparing the rank order of chosen centrality measure before and after the correction
Output	PC values for each node (in (1)(b) and (2)(b); The corrected centrality measure (for (1)(c) and (2)(c))
Methodological considerations	Communities should not overlap ((1) and (2)); (1) a Group affiliations may be ambiguous; (2) a Decision about appropriate community detection algorithm
Other analytical possibilities	PC version that treats positive and negative edges separately
Effect of reverse-coding variables	Not affected if signs are not taken in the account when calculating PC
Hypothesis/Research question	centrality measure is not affected by (pre-existing or data-driven) communities
MOTIF ANALYSIS
Recommended for network	(1) Not for networks with small number of nodes and/or very low density; (2) Has negative and positive ties; (3) If weighted, additional steps in the procedure
Important procedure steps	(a) Defining motifs of interest and the null model; (b) Motif identification and frequency; (c) Significance testing of motif frequency; If (3) is true: (d) Motif intensity (and coherence); (e) Significance testing of motif intensity (and coherence)
Output	Identified motifs; Motif Frequency; P-values for frequencies; Motif intensity (and coherence); P-values for the intensities (and coherence)
Methodological considerations	The definition of the null (reference) model
Other analytical possibilities	Other motif structures, e.g. that include more nodes
Effect of reverse-coding variables	Identified motifs and motif frequency will be differen, but onclusions about significance (of frequency, intensity, and coherence) will tend to converge
Hypothesis/Research question	Many research questions and hypotheses possible. In this study: Signed edges will tend to cluster in the line with what is observed in social networks and correlational networks (balance theory, forbidden triads, imbalanced triplets):= P0P, NNN, and PPN will be less frequent than expected by chance.; RQ1 = Do same pattern of results holds true when only relatively stronger motifs are considered?; RQ2= Are Intensity and Coherence measure following the same pattern of results as the frequency of motifs?

his should be the case, but there is a possibility that distances related to negative edges are present in a network in such a way that will not affect the MST construction, e.g. a weak negative tie that exists among two peripheral nodes that have ties to other more central node.