Network Duplication

<div><p>(A) A view of network duplication illustrating our representation of these networks. Nodes (genes) directly opposite each other are paralogs resulting from WGD. Given genes <i>n₁</i> and <i>n₂</i> and their respective paralogs <i>p₁</i> and <i>p₂, </i> redundant interactions (dashed lines) are those that occur more than once in the set <i>n₁</i>: <i>n₂, n₁</i>: <i>p₂, p₁</i>: <i>n₂</i>, and <i>p₁</i>: <i>p₂</i>. </p> <p>(B) Two statistics used to quantify these networks. Symmetry measures the degree to which one network partition has more interactions than the other. Redundancy measures the proportion of edges which have survived in more than one copy since duplication (see main text). Example values for the extant network in (A) are also given.</p> <p>(C) Network randomization via subgraph replacement. Each quartet of nodes is randomly replaced by one of the possible subgraphs with the same number of edges. Subgraph frequencies are dependent on the overall edge frequencies of the nodes.</p>