The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.
Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization
Open accessAbstract
Most of the distributed protocols for multi-agent consensus assume that the agents are mutually cooperative and “trustful,” and so the couplings among the agents bring the values of their states closer. Opinion dynamics in social groups, however, require beyond these conventional models due to ubiquitous competition and distrust between some pairs of agents, which are usually characterized by repulsive couplings and may lead to clustering of the opinions. A simple yet insightful model of opinion dynamics with both attractive and repulsive couplings was proposed recently by C. Altafini, who examined first-order consensus algorithms over static signed graphs. This protocol establishes modulus consensus, where the opinions become the same in modulus but may differ in signs. In this paper, we extend the modulus consensus model to the case where the network topology is an arbitrary time-varying signed graph and prove reaching modulus consensus under mild sufficient conditions of uniform connectivity of the graph. For cut-balanced graphs, not only sufficient, but also necessary conditions for modulus consensus are given.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Social Network Analysis: Methods and Applications
Wasserman, S., & Faust, K. (1994) · doi:10.1017/cbo9780511815478 · Cited by 17,557 · cited 2×
“[17], [18], which are usually modeled by repulsive couplings or negative ties [19] among the agents.”
BackgroundConsensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788 · cited 1×
“Unlike conventional consensus protocols [44] this influence may be either cooperative (when ajk > 0) or competitive (when ajk < 0).”
BackgroundDegroot, M. H. (1974) · Journal of the American Statistical Association · doi:10.1080/01621459.1974.10480137 · Cited by 4,004
Graph Theoretic Methods in Multiagent Networks
Mesbahi, M., & Egerstedt, M. (2010) · Princeton University Press eBooks · doi:10.1515/9781400835355 · Cited by 2,897 · cited 2×
“The properties of cooperative protocols (14) are widely known [1], [2], [49].”
BackgroundDistributed Consensus in Multi-vehicle Cooperative Control
Ren, W., & Beard, R. W. (2008) · Communications and Control Engineering · doi:10.1007/978-1-84800-015-5 · Cited by 2,826
Stability of multiagent systems with time-dependent communication links
Moreau, L. (2005) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.841888 · Cited by 2,706
Mixing beliefs among interacting agents
Deffuant, G., Neau, D., Amblard, F., & Weisbuch, G. (2000) · Advances in Complex Systems · doi:10.1142/s0219525900000078 · Cited by 2,165
Consensus Problems on Networks With Antagonistic Interactions
Altafini, C. (2013) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2012.2224251 · Cited by 2,109
On the Nature of Reactance and its Role in Persuasive Health Communication
Dillard, J. P., & Shen, L. (2005) · Communication Monographs · doi:10.1080/03637750500111815 · Cited by 1,571
Generalized gradients and applications
Clarke, F. H. (1975) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1975-0367131-6 · Cited by 1,206
Cited by
A tutorial on modeling and analysis of dynamic social networks. Part I
Proskurnikov, A. V., & Tempo, R. (2017) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2017.03.002 · Cited by 553
Self-citationA tutorial on modeling and analysis of dynamic social networks. Part II
Proskurnikov, A. V., & Tempo, R. (2018) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2018.03.005 · Cited by 294
Self-citation
Metadata
- Authors
- Proskurnikov, A. V., Matveev, A. S., & Cao, M.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2016-06
- Volume
- 61
- Issue
- 6
- Pages
- 1524-1536
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2206832235
- Cited by
- 357
- References
- 43
- FWCI
- 16.89
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization. https://app.cochat.ai/papers/10.1109/tac.2015.2471655
- The paper
- Proskurnikov, A. V., Matveev, A. S., & Cao, M. (2016). Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2015.2471655
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
