A twostep communication opinion dynamics model with selfpersistence and influence index for social networks based on the DeGroot model Abstract   Existing opinion dynamics models often fail to consider the relationship between one agent and people two degrees of separation from the agent. In addition, no accurate weight determination method has yet been fully developed. To address these limitations, this paper proposes a twostep communication opinion dynamics model based on the classical DeGroot model. Selfpersistence is introduced to measure the individualxe2x80x99s adherence to the initial opinion, and a new weight determination method proposed that instead of distributing the weights evenly, defines an influence index that is calculated from the selfpersistence and node degrees. To guide public opinion using the proposed opinion dynamics model, an optimization model is established by assuming a connected network; however, when the given network is not connected, a subnetwork recognition algorithm is developed and an edge adding algorithm is proposed to alter the structure. Three opinion control strategies are then used to control the opinion formation process. Numerical examples are given to verify the flexibility and practicality of the proposed opinion control strategies, and extensive simulations over random ER networks are given to provide insights into the parameter behavior of the three strategies.

A neighbour scale fixed approach for influence maximization in social networks Influence maximization is currently a most extensively researched topic in social network analysis. Existing approaches tackle this task by either pursuing the real influence strength of a node or designing proper measurements for estimating it. The degree is a popularly adopted influence strength metric, based on which a variety of methods have been developed. Though with good efficiency, degreebased methods suffer unsatisfactory accuracy since this metric only covers a limited considered scale over the whole network of interest and also lacks discriminatory power. In this paper, we propose a novel influence maximization method, named Fixed Neighbour Scale (FNS), which extracts useful information from multiple levels of neighbours for a target node to estimate its influence strength, rather than only considering directly connected neighbours as in degreebased methods. To facilitate the implementation of FNS, we also present a centrality measurement termed FNSdist, which estimates a nodexe2x80x99s influence strength by summing its multilevel neighboursxe2x80x99 weights that are mainly determined by their distances to the target node. Experiments conducted on nine networks of different sizes and categories show that the proposed FNS method achieves excellent and stable performance compared with other algorithms based on designing metrics for measuring influence strength. We also exhibit that FNSdist is a superior alternative centrality which is more proper and precise than the degree.