Attitudinal Network Graphs (ANG) are network graphs where edges capture an expressed opinion: two vertices connected by an edge can be agreeable (positive) or antagonistic (negative). Measure of consensus in attitudinal graph reflects how easy or difficult consensus can be reached that is acceptable by everyone. Frustration index is one such measure as it determines the distance of a network from a state of total structural balance. In this paper, we propose to measure the consensus in the graph by expanding the notion of frustration index to a frustration cloud, a collection of nearest balanced states for a given network. The frustration cloud resolves the consensus problem with minimal sentiment disruption, taking all possible consensus views over the entire network into consideration. A frustration cloud based approach removes the brittleness of traditional network graph analysis, as it allows one to examine the consensus on entire graph. A spanning-tree-based balancing algorithm captures the variations of balanced states and global consensus of the network, and enables us to measure vertex influence on consensus and strength of its expressed attitudes. The proposed algorithm provides a parsimonious account of the differences between strong and weak statuses and influences of a vertex in a large network, as demonstrated on sample attitudinal network graphs constructed from social and survey data. We show that the proposed method accurately models the alliance network, provides discriminant features for community discovery, successfully predicts administrator election outcome consistent with real election outcomes, and provides deeper analytic insights into ANG outcome analysis by pinpointing influential vertices and anomalous decisions.

中文翻译：

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通过挫折云表征态度网络图

态度网络图 (ANG) 是边捕捉表达意见的网络图：边连接的两个顶点可以是一致的（正）或对抗的（负）。态度图中的共识度量反映了达成共识的难易程度，这是每个人都可以接受的。挫折指数就是这样一种衡量标准，因为它决定了网络与总体结构平衡状态之间的距离。在本文中，我们建议通过将挫败指数的概念扩展到挫败云（给定网络的最近平衡状态的集合）来衡量图中的共识。挫折云以最小的情绪干扰解决了共识问题，将整个网络上所有可能的共识观点都考虑在内。基于挫折云的方法消除了传统网络图分析的脆弱性，因为它允许人们检查整个图的共识。基于生成树的平衡算法捕获网络平衡状态和全局共识的变化，并使我们能够衡量顶点对共识的影响及其表达态度的强度。所提出的算法对大型网络中强弱状态之间的差异以及顶点的影响提供了简洁的解释，如根据社会和调查数据构建的样本态度网络图所示。我们表明，所提出的方法准确地模拟了联盟网络，为社区发现提供了判别特征，成功地预测了与真实选举结果一致的管理员选举结果，