Understanding which nodes are most able to transmit or receive influence is a central problem in networked opinion dynamics, yet topology-only centrality measures do not account for heterogeneous susceptibility to social influence. We study source-specific, susceptibility-dependent influence in the Friedkin-Johnsen model on directed weighted networks. By treating fully stubborn agents as boundary nodes and the remaining agents as interior nodes, we formulate the dynamics as a discrete boundary-value problem. This formulation yields a Green operator and an all-source steady-state response matrix that quantify how a fixed opinion at each source propagates to every target. Building on this response matrix, we define influence-based broadcasting and reception measures that distinguish structural position from model-implied influence. We establish conditions for existence and uniqueness of the steady state, derive transient and steady-state representations, and characterize sensitivity to susceptibility parameters and perturbations of the influence network. For the undirected homogeneous-susceptibility specialization, we also provide a corresponding spectral analysis. Computational experiments on benchmark networks illustrate how heterogeneous susceptibility profiles shape response-based rankings and how these rankings differ from topology-only centralities. The framework provides a basis for studying influence propagation, source selection, and susceptibility-aware network intervention.
Sublinear-Time Algorithms for Diagonally Dominant Systems and Applications to the Friedkin-Johnsen Model
School of Computing and Data Science, The University of Hong Kong, China（香港大学计算机与数据科学学院）；School of Computer Science and Technology, University of Science and Technology of China, China（中国科学技术大学计算机科学与技术学院）
Opinion evolution in time-varying social influence networks with prejudiced agents
Delft University of Technology（代尔夫特理工大学）；Institute for Problems of Mechanical Engineering (IPME RAS)（俄罗斯科学院机械问题研究所）；ITMO University（ITMO大学）；CNR-IEIIT, Politecnico di Torino（都灵理工大学CNR-IEIIT研究所）；University of Groningen（格罗宁根大学）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）
Randomized opinion dynamics over networks: influence estimation from partial observations
Institute of Electronics, Computer and Telecommunication Engineering, National Research Council of Italy (CNR-IEIIT)（意大利国家研究委员会电子、计算机和通信工程研究所）；Department of Electrical Engineering at the Pennsylvania State University（宾夕法尼亚州立大学电气工程系）
Novel Multidimensional Models of Opinion Dynamics in Social Networks
V.A. Trapeznikov Institute for Control Sciences of Russian Academy of Sciences（俄罗斯科学院控制科学瓦·阿·特拉佩兹尼科夫研究所）；Institute for Problems of Mechanical Engineering of Russian Academy of Sciences（俄罗斯科学院机械工程学问题研究所）；ITMO University（ITMO大学）；University of Santa-Barbara（圣塔芭芭拉大学）；CNR-IEIIT, Politecnico di Torino（都灵理工大学意大利国家研究委员会信息工程研究所）
