Impact of degree mixing pattern on consensus formation in social networks

• A social network with more than 50,000 nodes is sampled from online social service “Twitter”.
• A degree mixing correlation is proposed to measure the randomness of the mixing pattern in detail.
• We show that specific structure property slows down the consensus formation process in social networks.

The consensus formation process in a social network is affected by a number of factors. This paper studies how the degree mixing pattern of a social network affects the consensus formation process. A social network of more than 50,000 nodes was sampled from the online social services website Twitter. Nodes in the Twitter user network are grouped by their in-degrees and out-degrees. A degree mixing correlation is proposed to measure the randomness of the mixing pattern for each degree group. The DeGroot model is used to simulate the consensus formation processes in the network. Simulation suggests that the non-random degree mixing pattern of social networks can slow down the rate of consensus.