Centrality is a fundamental building block in network analysis. Existing centrality measures focus on the network topology without considering nodal characteristics. However, this ignorance is perilous if the cascade payoff does not grow monotonically with the size of the cascade. In this paper, we propose a new centrality measure, Cascade Centrality, which integrates network position, the diffusion process, and nodal characteristics. It nests and spans the gap between degree, eigenvector, Katz, and diffusion centrality. Interestingly, when $p\lambda_1 > 1$, eigenvector, Katz and diffusion centrality all collapse to Cascade Centrality with a scaling factor determined by the distribution of eigenvector and the nodal influence vector. Furthermore, the presence of homophily in social networks enables the de-noising of real-world observations. Therefore, we propose a unified framework to simultaneously learn the actual nodal influence vector and network structure with an iterative learning algorithm. Experiments on synthetic and real data show that Cascade Centrality outperforms existing centrality measures in generating cascade payoffs. Moreover, with the proposed algorithm, the de-noised centrality measure is more correlated with the actual Cascade Centrality than merely computing from the observations. Cascade Centrality can capture more complex behaviors and processes in the network and has significant implications for theoretical studies in influence maximization and practical applications in viral marketing and political campaign.
from cs updates on arXiv.org https://ift.tt/2snxKMU
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