22 research outputs found
Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions
In this work we study the coupled dynamics of social balance and opinion
formation. We propose a model where agents form opinions under bounded
confidence, but only considering the opinions of their friends. The signs of
social ties -friendships and enmities- evolve seeking for social balance,
taking into account how similar agents' opinions are. We consider both the case
where opinions have one and two dimensions. We find that our dynamics produces
the segregation of agents into two cliques, with the opinions of agents in one
clique differing from those in the other. Depending on the level of bounded
confidence, the dynamics can produce either consensus of opinions within each
clique or the coexistence of several opinion clusters in a clique. For the
uni-dimensional case, the opinions in one clique are all below the opinions in
the other clique, hence defining a "left clique" and a "right clique". In the
two-dimensional case, our numerical results suggest that the two cliques are
separated by a hyperplane in the opinion space. We also show that the
phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and
Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the
context of politics, we comment about the possible relation of our results to
the fragmentation of an ideology and the emergence of new political parties.Comment: 8 figures, PLoS ONE 11(10): e0164323, 201
Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms
Social balance theory describes allowable and forbidden configurations of the
topologies of signed directed social appraisal networks. In this paper, we
propose two discrete-time dynamical systems that explain how an appraisal
network \textcolor{blue}{converges to} social balance from an initially
unbalanced configuration. These two models are based on two different
socio-psychological mechanisms respectively: the homophily mechanism and the
influence mechanism. Our main theoretical contribution is a comprehensive
analysis for both models in three steps. First, we establish the well-posedness
and bounded evolution of the interpersonal appraisals. Second, we fully
characterize the set of equilibrium points; for both models, each equilibrium
network is composed by an arbitrary number of complete subgraphs satisfying
structural balance. Third, we establish the equivalence among three distinct
properties: non-vanishing appraisals, convergence to all-to-all appraisal
networks, and finite-time achievement of social balance. In addition to
theoretical analysis, Monte Carlo validations illustrates how the non-vanishing
appraisal condition holds for generic initial conditions in both models.
Moreover, numerical comparison between the two models indicate that the
homophily-based model might be a more universal explanation for the formation
of social balance. Finally, adopting the homophily-based model, we present
numerical results on the mediation and globalization of local conflicts, the
competition for allies, and the asymptotic formation of a single versus two
factions
On the Structural Balance Dynamics Under Perceived Sentiment
In this letter, we propose a continuous-time dynamics for social network that represents patterns of both amity and enmity through directed signed graphs. The introduction of discrepancies between true and perceived sentiments gives rise to a non-autonomous system and distinguishes itself from the prior models. We show that for almost all initial configurations, the system will evolve into at most four factions. Under some mild assumptions on the initial conditions, structural balance with at most two factions can be achieved, which extends the previous results for symmetric or normal initial configurations without considering the effect of perceived sentiment
Signed Network Embedding with Application to Simultaneous Detection of Communities and Anomalies
Signed networks are frequently observed in real life with additional sign
information associated with each edge, yet such information has been largely
ignored in existing network models. This paper develops a unified embedding
model for signed networks to disentangle the intertwined balance structure and
anomaly effect, which can greatly facilitate the downstream analysis, including
community detection, anomaly detection, and network inference. The proposed
model captures both balance structure and anomaly effect through a low rank
plus sparse matrix decomposition, which are jointly estimated via a regularized
formulation. Its theoretical guarantees are established in terms of asymptotic
consistency and finite-sample probability bounds for network embedding,
community detection and anomaly detection. The advantage of the proposed
embedding model is also demonstrated through extensive numerical experiments on
both synthetic networks and an international relation network.Comment: 24 pages, 4 figures. The appendix containing technical proof is not
included, but will be uploaded in the futur
The structure of gene-gene networks beyond pairwise interactions
Despite its high and direct impact on nearly all biological processes, the
underlying structure of gene-gene interaction networks is investigated so far
according to pair connections. To address this, we explore the gene interaction
networks of the yeast Saccharomyces cerevisiae beyond pairwise interaction
using the structural balance theory (SBT). Specifically, we ask whether
essential and nonessential gene interaction networks are structurally balanced.
We study triadic interactions in the weighted signed undirected gene networks
and observe that balanced and unbalanced triads are over and underrepresented
in both networks, thus beautifully in line with the strong notion of balance.
Moreover, we note that the energy distribution of triads is significantly
different in both essential and nonessential networks compared with the
shuffled networks. Yet, this difference is greater in the essential network
regarding the frequency as well as the energy of triads. Additionally, results
demonstrate that triads in the essential gene network are more interconnected
through sharing common links, while in the nonessential network they tend to be
isolated. Last but not least, we investigate the contribution of all-length
signed walks and its impact on the degree of balance. Our findings reveal that
interestingly when considering longer cycles the nonessential gene network is
more balanced compared to the essential network.Comment: 16 pages, 5 figures, 4 table