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In complex networks the degrees of adjacent nodes may often appear dependent-- which presents a modelling challenge. We present a working framework forstudying networks with an arbitrary joint distribution for the degrees ofadjacent nodes by showing that such networks are a special case ofedge-coloured random graphs. We use this mapping to study bond percolation innetworks with assortative mixing and show that, unlike in networks withindependent degrees, the sizes of connected components may feature unexpectedsensitivity to perturbations in the degree distribution. The results alsoindicate that degree-degree dependencies may feature a vanishing percolationthreshold even when the second moment of the degree distribution is finite.These results may be used to design artificial networks that efficientlywithstand link failures and indicate possibility of super spreading in networkswithout clearly distinct hubs

Networks with degree-degree correlations is a special case of edge-coloured random graphs