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A signed graph is called balanced if each of its cycles includes an even number of negative edges. Balance is often characterized by the frustration index or by finding a single convergent balanced state of network consensus. In this paper, we propose to expand the measures of consensus from a single balanced state associated with the frustration index to the set of nearest balanced states. We introduce the<jats:italic>frustration cloud<\/jats:italic>as a set of all nearest balanced states and use a graph-balancing algorithm to find all nearest balanced states in a deterministic way. Computational concerns are addressed by measuring consensus probabilistically, and we introduce new vertex and edge metrics to quantify<jats:italic>status<\/jats:italic>,<jats:italic>agreement<\/jats:italic>, and<jats:italic>influence<\/jats:italic>. We also introduce a new global measure of controversy for a given signed graph and show that vertex status is a zero-sum game in the signed network. We propose an efficient scalable algorithm for calculating frustration cloud-based measures in social network and survey data of up to 80,000 vertices and half-a-million edges. We also demonstrate the power of the proposed approach to provide discriminant features for community discovery when compared to spectral clustering and to automatically identify dominant vertices and anomalous decisions in the network.<\/jats:p>","DOI":"10.1007\/s10618-021-00795-z","type":"journal-article","created":{"date-parts":[[2021,9,24]],"date-time":"2021-09-24T11:26:59Z","timestamp":1632482819000},"page":"2498-2539","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Characterizing attitudinal network graphs through frustration cloud"],"prefix":"10.1007","volume":"35","author":[{"given":"Lucas","family":"Rusnak","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9972-9760","authenticated-orcid":false,"given":"Jelena","family":"Te\u0161i\u0107","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,24]]},"reference":[{"issue":"1","key":"795_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/bs.3830030102","volume":"3","author":"RP Abelson","year":"1958","unstructured":"Abelson RP, Rosenberg MJ (1958) Symbolic psycho-logic: a model of attitudinal cognition. 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