Table 1 Details of centrality metrics Insights into the literature show that network edges are critical communication chan- nels. However, the contribution of all edges is assumed to be the same in centrality met- rics based on unweighted networks, where this is an unrealistic assumption of interactions between users. To prove the effectiveness of weighted edges in measuring influence, we define Reputation-Optimism (RO) index. “Reputation” indicates the popularity of a user in the network and “Optimism” indicates the higher following of other users. RO in an undi- rected network for an edge between nodes u and v is defined by Eq. (2). To further clarify the computational procedure of the proposed LASPN metric, we describe a numerical example. An undirected and unweighted graph with 10 nodes and 13 edges is assumed as shown in Fig. 2. We give an example of calculating LASPN(v) for v = 3 at L = 2 and w,,, = RO,,,. According to definition 1; @,,,.;(3) = 0.5, because k, = 5 and N = 10. According to definition 2; @gonj_rocai(3) is calculated by the Eq. (12). 4 Experimental results and analysis achieves the best performance with L = 3, and the results with L = 2 are also promising. Hence, other experiments are performed based on this level of neighborhood for LASPN. The research society shows strong evidence of the significant impact of edges on cen- trality metrics (Kang et al. 2016). However, most centrality metrics consider the contribu- tion of edges to be the same, which is an unrealistic assumption of interactions between users. To prove the effectiveness of weighted edges in influence estimation and also to find the best effectiveness for LASPN, we compare several different weight indexes. The pro- posed weights include connection strength, local and global characteristics along with the frequency of interactions between users. In addition to RO index, we consider Common Neighbors (CN) (Lorrain and White 1971), Jaccard Coefficient (JC) (Jaccard 1901), and FriendLink (FL) (Papadimitriou et al. 2012) as edge weights. These indexes are defined by Eqs. (24-26). Fig. 3 Results of Kendall’s ¢ coefficient for LASPN and classical centrality metrics in different complex networks Anew semi-local centrality for identifying influential nodes... Fig.4 Results of Kendall’s ¢ coefficient for LASPN and state-of-the-art centrality metrics in different com- plex networks
