Correlated randomly growing graphs

We introduce a new model of correlated randomly growing graphs and study the fundamental questions detecting correlation estimating aspects structure. The is simple starts with any graphs, such as uniform attachment (UA) or preferential (PA). Given model, pair (G1,G2) grown in two stages: until time t⋆ they are together (i.e., G1=G2), after which grow independently according to underlying growth model. show that whenever seed graph has an influence model—this been shown for PA UA trees conjectured hold broadly—then can be detected this even if just single step. also give general sufficient condition (which holds trees) under detection possible probability going 1 t⋆→∞. Finally, we amount correlation, measured by t⋆, estimated vanishing relative error