Mapping the semi-nested community structure of 3D chromosome contact networks
Fig 1
Three examples of nestedness (Nij) in a simple bipartite network.
The networks in panels (a)–(c) have the same number of nodes in each layer—18 domains (small circles) and two communities (i and j, large circles)—and the same number of links (18) but connected differently to achieve varying nestedness. Below each network, we illustrate how we calculate Nij using Eqs (4)–(7). On the horizontal k-axis, we indicate the number of shared nodes Sij for the community pair and the expected overlap μij calculated from Eq (3). The panels (a)–(c) show three essential Nij regimes (μij = 4 for all of the cases). (a) Mostly segregated (Sij < μij, Nij = −0.5). Because Sij = 2 and μij = 4, the i and j communities are half-way to full segregation. We illustrate this with a dark-blue stripe covering half the 0 ≤ k ≤ 4 = μij range. (b) Random overlap (Sij = μij, Nij = 0). The number of shared nodes equals the random expectation. (c) Mostly nested (Sij > μij, Nij = 0.5). Here i and j share one domain more than expected (Sij = 5). This yields Nij = 0.5 because their overlap is at the midpoint between the random and the maximum overlap (Sij = 6) that would result in ideal nesting (Nij = 1). We illustrate this with the orange stripe spanning half of the range μij(= 4) ≤ k ≤ 6. This example shows that Nij measures the relative overlap compared to what is achievable given the link density rather than absolute numbers.