Fig. 4

Analysis of the weighted graph distance. a Hi-C contact map of a 10Mb-fragment of human chromosome 1 (1kb-resolution data from [3] binned at a resolution of 10kb, axes in Mb), in the form of a heat map where the color code represents the contact frequency (− log10 units). b Log-log scatter plot of the shortest-path distances D _ij with respect to the contact frequencies F _ij , for two values α=0.2 (top) and α=1 (bottom) of the exponent α involved in the prescription of the edge length. The upper boundary of the cloud of points is a line of slope −α, corresponding to the pairs of sites for which the direct edge (i,j) of length L _ij is the shortest path. Minus the slope of the red line gives the exponent α _Sh of the best power-law fit \(D_{ij}\sim F_{ij}^{-\alpha _{Sh}}\). c Increase of the percentage N _Sh of pairs of sites for which the direct connection (i,j) is not the shortest path, when α increases. d Exponent α _Sh as a function of α; the dashed blue line indicates the diagonal α _Sh =α