24The rapid advancement of single cell technologies has shed new light on the complex 25 mechanisms of cellular heterogeneity. However, compared with bulk RNA sequencing 26 (RNA-seq), single-cell RNA-seq (scRNA-seq) suffers from higher noise and lower 27 coverage, which brings new computational difficulties. Based on statistical 28 independence, cell-specific network (CSN) is able to quantify the overall associations 29 between genes for each cell, yet suffering from a problem of overestimation related to 30 indirect effects. To overcome this problem, we propose the "conditional cell-specific 31 network" (CCSN) method, which can measure the direct associations between genes 32 by eliminating the indirect associations. CCSN can be used for cell clustering and 33 dimension reduction on a network basis of single cells. Intuitively, each CCSN can be 34 viewed as the transformation from less "reliable" gene expression to more "reliable" 35 gene-gene associations in a cell. Based on CCSN, we further design network flow 36 entropy (NFE) to estimate the differentiation potency of a single cell. A number of 37 scRNA-seq datasets were used to demonstrate the advantages of our approach: (1) one 38 direct association network for one cell; (2) most existing scRNA-seq methods designed 39 for gene expression matrices are also applicable to CCSN-transformed degree matrices; 40 (3) CCSN-based NFE helps resolving the direction of differentiation trajectories by 41 quantifying the potency of each cell. CCSN is publicly available at 42 http://sysbio.sibcb.ac.cn/cb/chenlab/soft/CCSN.zip. 43 44 45 KEYWORDS: Single cell analysis; Network flow entropy; Cell-specific network; 46 Single cell network; Direct association; Conditional independence 47 49 With the development of high-throughput single-cell RNA sequencing (scRNA-seq), 50 novel cell populations in complex tissues [1-5] can be identified and the differentiation 51 trajectory of cell states [6-8] can be obtained, which opens a new way to understand the 52 heterogeneity and transition of cells [9-11]. However, compared to traditional bulk 53RNA-seq data, the prevalence of high technical noise and dropout events is a major 54 problem in scRNA-seq [12][13][14][15][16][17], which raises substantial challenges for data analysis. 55Many computational methods were proposed to improve the identification of new cell 56 types [18][19][20][21]. Meanwhile, imputation is an effective strategy to transform the dropouts 57 to the substituted values [22][23][24][25][26]. However, most of these methods mainly analyze 58 mRNA expression/concentrations, while the information of gene-gene interactions (or 59 their network) is ignored. 60Recently, a network-based method, cell-specific network (CSN), was proposed to 61 perform network analysis for scRNA-seq data [27], which elegantly infers a network 62 for each cell and successfully transforms the noisy and "unreliable" gene expression 63 data to the more "reliable" gene association data. The network degree matrix (NDM) 64 derived from CSN can be furt...