Network comparison of single cells (from sequencing data) What methods can we use to compare networks (PPI, gene regulatory etc) created from single-cell gene expression (or proteomics) data?

There are methods that construct networks by comparing two conditions (e.g. from (gene) co-expression, or differential gene correlation (DGCA, Differential Gene Correlation Analysis)), and infer properties based on these networks.

What I'm interested here is the comparison of networks constructed for each single cell. The networks can be constructed solely from the data, or  using known interactions (edges) with the help of a database. These comparisons could be used for understanding or classifying cells.

This will probably require a network construction method (which may be hard because we do not have replicates for single cells), some form of network similarity measure / network alignment method. This is a very hard task in general, but here we have 1-to-1 correspondence for each node between the cells (networks), which should help.

Similar discussions at 


Biostars: Question: How Do You Align Or Compare Two Networks
Content-Wise?
Researchgate: How can I measure similarity between two networks?


One related paper for single-cells is Chan et al., 2017, which uses groups of cells (created by other methods, e.g. clustering) to construct networks, and manually compares them (common edges / Venn diagram).
You can't build a network of a single cell only with the expression of a single cell. You either need previous known interactions or pathways or you need to use several cells/samples.
If you use previous known information, you can use pathway information, otherwise you can group some cells and use something along the lines of WGCNA to find a scale-free network.

In the first case one can add the expression upon it and see what is happening, what edges are kept and which ones not...



Once you have the network for each cell you can compare the metrics for each cell. Some metrics to look at are the centrality of each gene and the betweneess.
In a more general way, you can look if it follows a scale-free topology or other type of network structures, or how many nodes are present, how many edges are present...