EGLASSO is an adapted version of GLASSO for incorporating the hub gene information. The EGLASSO maximizes $$log|\Omega| -tr(S\Omega) -\alpha\lambda \sum_{ i < j, \left \{ i\in H\right \}\cup \left \{ j\in H\right \}}|\omega_{ij}| - \lambda\sum_{i < j, i,j\in H^{c}}|\omega^{ij}| ,$$ where $\lambda \geq 0$ and $0 \leq \alpha \leq 1$ are two tuning parameters, $S$ is the sample covariance matrix, $tr(A)$ is the trace of $A$ and $H$ is the set of hub nodes that were previously identified.

Reference:
1. Donghyeon Yu, Johan Lim, Xinlei Wang, Faming Liang, and Guanghua Xiao. "Enhanced construction of gene regulatory networks using hub gene information." BMC bioinformatics 18.1 (2017): 186.

Note:
1. Change the $\lambda$ value $(\lambda > 0)$ to control the sparsity of network. A larger $\lambda$ will give you more a sparse network. If you don't know how to choose a value, use the default one.
2. Change the $\alpha$ value $(0 \leq \alpha \leq 1)$ to control the penalty on hub genes. A smaller $\alpha$ will give less penalty on edges connected to hub genes. If you don't know how to choose a value, use the default one.
3. The hub gene input should be gene names separated by a comma, e.g. "Gene13,Gene52,Gene199". All the gene names must be contained in column names of the expression data.