Table 1.

Measures of expression and network topology that potentially characterize the essentiality of a transcription factor in a gene-regulatory network

Topological property	Abbrev.	Description	Reference
Global Connectivity	GC	number of local networks in which gene is found
Degree	k	number of edges incident to a gene, normalized by size of the neighborhood (k/N)
Proportion Predicted Targets	T	proportion of incident edges annotated by predicted binding
Weighted Clustering Coefficient*	CCw	$C{C}_i=\frac{E_i}{k_i\left(k_i-1\right)}$	[42]
Weighted Closeness Centrality†	C	$C_i=\frac{n-1}{{\Sigma }_{j\in V}{{\setminus }_{}}_i{d}_G\left(i,j\right)}$	[43]
Absolute Expression
Proerythroblast	P	Average expression across replicates
Basophilic Erythroblast	B	Average expression across replicates
Polyorthochromatic Erythroblast	O	Average expression across replicates
Reticulocyte	R	Average expression across replicates
Differential Expression
Profile Shape‡	PS	Best-fit vector mapped to the average expression profile
Maximum Ratio	MR	Ratio of maximum to minimum expression during developmental series

* ratio of the number of edges that exist between the k neighbors of gene i (E_i) and the number of potential edges between the neighbors, or k_i(k_i − 1).

^† reciprocal of the mean shortest path length between a gene i and all other genes that can be reached from it, where V is the set of all possible genes and d_G is the shortest path length between genes i and j. Path lengths were estimated using the Dijkstra distance [44] as implemented in the Boost Graph Library [45].

^‡ Average expression profiles mapped to 28 templates using vector projection. The best-fit profile (PS) was used as an indicator of the trend in expression during erythropoiesis.