Second-Order Assortative Mixing in Social Networks

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In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node's importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e. if two nodes are connected, they tend to have similar node degrees, suggesting that people tend to mix with those of comparable prominence. In this paper, we report the second-order assortative mixing in social networks. If two nodes are connected, we measure the degree correlation between their most prominent neighbours, rather than between the two nodes themselves. We observe very strong second-order assortative mixing in social networks, often significantly stronger than the first-order assortative mixing. This suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same. This is also true if we measure the average prominence of neighbours of the two people. This property is weaker or negative in non-social networks. We investigate a number of possible explanations for this property. However, none of them was found to provide an adequate explanation. We therefore conclude that second-order assortative mixing is a new property of social networks.