Matrix-scaled consensus on socfb-Amherst41 dataset

We perform the matrix-scaled consensus (MSC) algorithm [1,2] on the dataset socfb-Amherst41 [3]. The dataset is available for download at [4].

1. The network attracted from the dataset is used as the interaction graph for the simulation. The graph is undirected, connected and contains 2235 vertices and 90954 edges.
2. We assume that the people in the network are classified into five major groups based on their religion beliefs (No religion, Buddhism & Folk religion, Hinduism, Islam, Christianity). Since the dataset does not provide each individual's religion, we use randomization to assign each individual into 5 groups. The probability for an idividual to be classified with a given religion is derived from the data in []
3. Each group is assigned a corresponding 2x2 SO(2) scaling matrix. The non-religion group is assigned with the 2x2 identity matrix. Three factors are considered for determining the scaling matrix of the other groups: God(s), Afterlife, and Attitude towards alcohol  as described in the Table 1 (a '+' corresponding to a +pi/4 rotation CCW, and a '-' corresponds to a -pi/4 rotation CCW).The references for these factors can be found at [6].
4. The simulation results include: the network with colors indicating religion groups; the initial opinion vectors [x_i; y_i] of the 2235 agents are randomly generated (x_i, y_i take values between 0 and 1), and snapshots of the simulations at severral time instant between 0 to 10 seconds.

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Criteria \ Group |     No religion   |      Buddism & Folklore religion  |               Hinduism              |                Islam                |             Christianity           |

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God(s)               |           No         |       Multiple Gods (+)       |                Multiple Gods (+)              |            One God (-)          |           One God  (-)       |

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Afterlife              |          No       |    Rebirth or nirvana (+)   |  Reincarnation until attaining liberation (+)  |    Paradise or Hell (-)     |   Heaven or Hell (-)   |

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Alcohol              |  No prefference  |       Prohibited (-)      |        No prohibition  (+)         |        Not allowed (-)        |         No prohibition (+)        |

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Scaling matrix   |       eye(2)         |       Rot(+\pi/4)     |       Rot(+3\pi/4)       |      Rot(-3\pi/4)       |       Rot(-\pi/4)     | 

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Table 1: Comparison of 5 major religious groups based on three criteria. A "+" means more openess and a "-" means more conservative. Each '+' accounts for +pi/4 CCW rotation and each '-' accounts for a -pi/4 CCW rotation in the scaling matrix.

References

[1] Trinh, M. H., Vu, D. V., Tran, Q. V., and Ahn, H.-S. "Matrix-scaled consensus." In Proc. of the 61st IEEE Conference on Decision and Control (CDC), pp. 346-351. IEEE, 2022. arXiv preprint arXiv:2204.10723 (2022)

[2] Trinh, M. H., Vu, H. H., Le-Phan, N.-M., and Nguyen, Q. N. "Matrix-Scaled Consensus over Undirected Networks." arXiv preprint arXiv:2303.14751 (2023).

[3] Rossi, Ryan, and Nesreen Ahmed. "The network data repository with interactive graph analytics and visualization." In Proceedings of the AAAI conference on artificial intelligence, vol. 29, no. 1. 2015.

[4] https://networkrepository.com/socfb-Amherst41.php

[5] https://en.wikipedia.org/wiki/Major_religious_groups

[6] https://religionfacts.com/big-religion-chart