Degree of an edge and Platt Number in signed networks

Diviya K D, Anjaly Kishore

Abstract


Positive labelled edges play a vital role in network analysis.The degree of edges in signed graphs is introduced by giving importance to
positive edges incident on the end vertices of that edge. The concept
of Platt number of a graph, which is the sum of degrees of its edges, is
extended to signed graphs based on the degree defined. Bounds of degree of an edge and Platt number in certain classes of signed graphs
are determined. Some characterizations on Platt number of signed
graphs are also established. A model to analyse social networks using degree of edges and Platt number is also proposed.
Keywords: Signed graph, positive edges, negative edges, networks,
information diffusion, degree of an edge, Platt number

Keywords


Signed graph, positive edges, negative edges, networks, information diffusion, degree of an edge, Platt number

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References


Acharya, B. D. Acharya, M. Acharya, and D. Sinha. Characterization of a

signed graph whose signed line graph is s-consistent. Bull. Malaysian Math.

Sci. Soc.(2), 2009.

B. D. Acharya. Applications of sigraphs in behavioral sciences. MRI Tech.

Rep. No. DST/HCS/409/79, 1985.

B. D. Acharya. New algebraic models of social systems. Indian J. Pure

Appl. Math., 17(2):150–168, 1986.

P. Anchuri and M. Magdon-Ismail. Communities and balance in signed networks: A spectral approach. In 2012 IEEE/ACM International Conference

on Advances in Social Networks Analysis and Mining, pages 235–242, 2012.

doi: 10.1109/ASONAM.2012.48.

M. M. Belavadi and T. A. Mangam. Platt number of total graphs. International Journal of Applied Mathematics, 31(5):593, 2018.

D. Cartwright and F. Harary. Structural balance: a generalization of heider’s

theory. Psychological review, 63(5):277, 1956.

A. Gionis, A. Matakos, B. Ordozgoiti, and H. Xiao. Mining signed networks:

Theory and applications: Tutorial proposal for the web conference 2020. In

Companion Proceedings of the Web Conference 2020, pages 309–310, 2020.

A. Guille, H. Hacid, C. Favre, and D. A. Zighed. Information diffusion in

online social networks: A survey. ACM Sigmod Record, 42(2):17–28, 2013.

F. Harary and R. Z. Norman. Graph theory as a mathematical model in

social science. Number 2. University of Michigan, Institute for Social Research Ann Arbor, MI, 1953.

F. Harary, R. Z. Norman, and D. Cartwright. Structural models: An introduction to the theory of directed graphs. Wiley, 1965.

M. S. Jalali, A. Ashouri, Herrera-Restrepo, and H. Zhang. Information diffusion through social networks: The case of an online petition. Expert Systems

with Applications, 44:187–197, 2016.

D. Li, W. Wang, C. Jin, J. Ma, X. Sun, Z. Xu, S. Li, and J. Liu. User recommendation for promoting information diffusion in social networks. Physica

A: Statistical Mechanics and its Applications, 534:121536, 2019.

P. Mahadevi, A. Babu, and J. B. Babujee. Platt number for some chemical

graphs and general results. International Journal of Mathematics Trends and

Technology(IJMTT), 2018.

J. R. Platt. Influence of neighbor bonds on additive bond properties in paraffins. The Journal of Chemical Physics, 15(6):419–420, 1947.

X. Rui, F. Meng, Z. Wang, G. Yuan, and C. Du. Spir: The potential spreaders

involved sir model for information diffusion in social networks. Physica A:

Statistical Mechanics and its Applications, 506:254–269, 2018.

R. Sun, C. Chen, X. Wang, Y. Zhang, and X. Wang. Stable community

detection in signed social networks. IEEE Transactions on Knowledge and

Data Engineering, pages 1–1, 2020. doi: 10.1109/TKDE.2020.3047224.

J. Tang, Y. Chang, C. Aggarwal, and H. Liu. A survey of signed network

mining in social media. ACM Computing Surveys (CSUR), 49(3):1–37,

A. Tselykh, V. Vasilev, L. Tselykh, and F. A. Ferreira. Influence control

method on directed weighted signed graphs with deterministic causality. Annals of Operations Research, pages 1–25, 2020.

T. Zaslavsky. A mathematical bibliography of signed and gain graphs and allied areas. The Electronic Journal of Combinatorics, pages DS8–Dec, 2012




DOI: http://dx.doi.org/10.23755/rm.v46i0.1061

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