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  .
Attitudinal Network Graphs are signed graphs where edges capture an expressed opinion: two vertices connected by an edge can be agreeable (positive) or antagonistic (negative). A signed graph is called balanced if each of its cycles includes an even number of negative edges. Balance is often characterized by frustration index or by finding a single convergent balanced state i.e. network consensus. In this paper, we propose to expand the measures of consensus from a single balanced state associated to the frustration index to the set of nearest balanced states . We introduce the frustration cloud as a set of all nearest balanced states, and use a graph balancing algorithm to find all nearest balanced states in deterministic way. Computational concerns are addressed by measuring consensus probabilistically, and we introduce new vertex and edge metrics to quantify status, agreement, and influence. We introduce 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, and we 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 .
R
(ANG) are network
are signed
R
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.
A signed graph is called balanced if each of its cycles includes an even number of negative edges. Balance is often characterized by frustration index or by finding a single convergent balanced state i.e. network consensus.
R
measure the consensus in the graph by expanding the notion of
expand the measures of consensus from a single balanced state associated to the
R
a frustration cloud, a collection
the set
R
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
. We introduce the frustration cloud as a set of all nearest balanced states, and use a graph balancing algorithm to find all nearest balanced states in deterministic way. Computational concerns are addressed by measuring consensus probabilistically, and we introduce new vertex
A
edge metrics to quantify status, agreement, and influence. We introduce 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
R
. We show that the proposed method accurately models the alliance network, provides
of up to 80,000 vertices and half-a-million edges, and we demonstrate the power of the proposed approach to provide
R
, successfully predicts administrator election outcome consistent with real election outcomes, and provides deeper analytic insights into ANG outcome analysis by pinpointing influential
when compared to spectral clustering and to automatically identify dominant
A
in the network