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1. Spheres of Legislation: Polarization and Most Influential Nodes in Behavioral Context

   https://doi.org/10.1007/978-3-030-36683-4_6  

   Phillips, Andrew C; Irfan, Mohammad T; Ostertag-Hill, Luca. (January 2020, Studies in computational intelligence)

   Game-theoretic models of influence in networks often assume the network structure to be static. In this paper, we allow the network structure to vary according to the underlying behavioral context. This leads to several interesting questions on two fronts. First, how do we identify different contexts and learn the corresponding network structures using real-world data? We focus on the U.S. Senate and apply unsupervised machine learning techniques, such as fuzzy clustering algorithms and generative models, to identify different spheres of legislation as context and learn an influence network for each sphere. Second, how do we analyze these networks in order to gain an insight into the role played by the spheres of legislation in various interesting constructs like polarization and most influential nodes? To this end, we apply both game-theoretic and social network analysis techniques. In particular, we show that game-theoretic notion of most influential nodes brings out the strategic aspects of interactions like bipartisan grouping, which typical centrality measures fail to capture. We also show that for the same set of senators, some spheres of legislation are more polarizing than others. 

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2. Discerning Edge Influence for Network Embedding

   https://doi.org/10.1145/3357384.3358044  

   Wang, Yaojing; Yao, Yuan; Tong, Hanghang; Xu, Feng; Lu, Jian (November 2019, CIKM)

   Network embedding, which learns the low-dimensional representations of nodes, has gained significant research attention. Despite its superior empirical success, often measured by the prediction performance of downstream tasks (e.g., multi-label classification), it is unclear why a given embedding algorithm outputs the specific node representations, and how the resulting node representations relate to the structure of the input network. In this paper, we propose to discern the edge influence as the first step towards understanding skip-gram basd network embedding methods. For this purpose, we propose an auditing framework NEAR, whose key part includes two algorithms (NEAR-ADD and NEAR-DEL) to effectively and efficiently quantify the influence of each edge. Based on the algorithms, we further identify high-influential edges by exploiting the linkage between edge influence and the network structure. Experimental results demonstrate that the proposed algorithms (NEAR-ADD and NEAR-DEL) are significantly faster (up to 2, 000×) than straightforward methods with little quality loss. Moreover, the proposed framework can efficiently identify the most influential edges for network embedding in the context of downstream prediction task and adversarial attacking. 

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3. Finding influential nodes in networks using pinning control: Centrality measures confirmed with electrochemical oscillators

   https://doi.org/10.1063/5.0163899  

   Bomela, Walter; Sebek, Michael; Nagao, Raphael; Singhal, Bharat; Kiss, István Z; Li, Jr-Shin (September 2023, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   The spatiotemporal organization of networks of dynamical units can break down resulting in diseases (e.g., in the brain) or large-scale malfunctions (e.g., power grid blackouts). Re-establishment of function then requires identification of the optimal intervention site from which the network behavior is most efficiently re-stabilized. Here, we consider one such scenario with a network of units with oscillatory dynamics, which can be suppressed by sufficiently strong coupling and stabilizing a single unit, i.e., pinning control. We analyze the stability of the network with hyperbolas in the control gain vs coupling strength state space and identify the most influential node (MIN) as the node that requires the weakest coupling to stabilize the network in the limit of very strong control gain. A computationally efficient method, based on the Moore–Penrose pseudoinverse of the network Laplacian matrix, was found to be efficient in identifying the MIN. In addition, we have found that in some networks, the MIN relocates when the control gain is changed, and thus, different nodes are the most influential ones for weakly and strongly coupled networks. A control theoretic measure is proposed to identify networks with unique or relocating MINs. We have identified real-world networks with relocating MINs, such as social and power grid networks. The results were confirmed in experiments with networks of chemical reactions, where oscillations in the networks were effectively suppressed through the pinning of a single reaction site determined by the computational method. 

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4. Theoretical and Computational Characterizations of Interaction Mechanisms on Facebook Dynamics Using a Common Knowledge Model

   https://doi.org/10.1007/s13278-021-00791-7  

   Kuhlman, Chris J; Korkmaz, Gizem; Ravi, S S; Vega-Redondo, Fernando (October 2021, Social network analysis and mining)

   Web-based interactions enable agents to coordinate and generate collective action. Coordination can facilitate the spread of contagion to large groups within networked populations. In game theoretic contexts, coordination requires that agents share common knowledge about each other. Common knowledge emerges within a group when each member knows the states and the thresholds (preferences) of the other members, and critically, each member knows that everyone else has this information. Hence, these models of common knowledge and coordination on communication networks are fundamentally different from influence-based unilateral contagion models, such as those devised by Granovetter and Centola. Moreover, these models utilize different mechanisms for driving contagion. We evaluate three mechanisms of a common knowledge model that can represent web-based communication among groups of people on Facebook, using nine social (media) networks. We provide theoretical results indicating the intractability in identifying all node-maximal bicliques in a network, which is the characterizing network structure that produces common knowledge. Bicliques are required for model execution. We also show that one of the mechanisms (named PD2) dominates another mechanism (named ND2). Using simulations, we compute the spread of contagion on these networks in the Facebook model and demonstrate that different mechanisms can produce widely varying behaviors in terms of the extent of the spread and the speed of contagion transmission. We also quantify, through the fraction of nodes acquiring contagion, differences in the effects of the ND2 and PD2 mechanisms, which depend on network structure and other simulation inputs. 

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5. Top-L Most Influential Community Detection Over Social Networks

   Zhang, N; Ye, Y; Lian, X; Chen, M (May 2024, IEEE)

   In many real-world applications such as social network analysis and online marketing/advertising, community detection is a fundamental task to identify communities (subgraphs) in social networks with high structural cohesiveness. While previous works focus on detecting communities alone, they do not consider the collective influences of users in these communities on other user nodes in social networks. Inspired by this, in this paper, we investigate the influence propagation from some seed communities and their influential effects that result in the influenced communities. We propose a novel problem, named Top-L most Influential Community DEtection (TopL-ICDE) over social networks, which aims to retrieve top-L seed communities with the highest influences, having high structural cohesiveness, and containing user-specified query keywords. To efficiently tackle the TopL-ICDE problem, we design effective pruning strategies to filter out false alarms of seed communities and propose an effective index mechanism to facilitate efficient Top-L community retrieval. We develop an efficient TopL-ICDE answering algorithm by traversing the index and applying our proposed pruning strategies. We also formulate and tackle a variant of TopL-ICDE, named diversified top-L most influential community detection (DTopL-ICDE), which returns a set of L diversified communities with the highest diversity score (i.e., collaborative influences by L communities). We prove that DTopL-ICDE is NP-hard, and propose an efficient greedy algorithm with our designed diversity score pruning. Through extensive experiments, we verify the efficiency and effectiveness of our proposed TopL-ICDE and DTopL-ICDE approaches over real/synthetic social networks under various parameter settings. 

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