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We study properties of some standard network models when the population issplit into two types and the connection pattern between the types is varied.The studied models are generalizations of the Erd\H{o}s-R\'{e}nyi graph, theconfiguration model and a preferential attachment graph. For theErd\H{o}s-R\'{e}nyi graph and the configuration model, the focus is on thecomponent structure. We derive expressions for the critical parameter,indicating when there is a giant component in the graph, and study the size ofthe largest component by aid of simulations. When the expected degrees in thegraph are fixed and the connections are shifted so that more edges connectvertices of different types, we find that the critical parameter decreases. Thesize of the largest component in the supercritical regime can be bothincreasing and decreasing as the connections change, depending on thecombination of types. For the preferential attachment model, we analyze thedegree distributions of the two types and derive explicit expressions for thedegree exponents. The exponents are confirmed by simulations that alsoillustrate other properties of the degree structure.

Birds of a feather or opposites attract - effects in network modelling