TY - JOUR

T1 - Diverse phase transitions in optimized directed network models with distinct inward and outward node weights

AU - Chang, Rong Chih

AU - Cheng, An Liang

AU - Lai, Pik Yin

N1 - Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/3

Y1 - 2023/3

N2 - We consider growing directed network models that aim at minimizing the weighted connection expenses while at the same time favoring other important network properties such as weighted local node degrees. We employed statistical mechanics methods to study the growth of directed networks under the principle of optimizing some objective function. By mapping the system to an Ising spin model, analytic results are derived for two such models, exhibiting diverse and interesting phase transition behaviors for general edge weight, inward and outward node weight distributions. In addition, the unexplored cases of negative node weights are also investigated. Analytic results for the phase diagrams are derived showing even richer phase transition behavior, such as first-order transition due to symmetry, second-order transitions with possible reentrance, and hybrid phase transitions. We further extend previously developed zero-temperature simulation algorithm for undirected networks to the present directed case and for negative node weights, and we can obtain the minimal cost connection configuration efficiently. All the theoretical results are explicitly verified by simulations. Possible applications and implications are also discussed.

AB - We consider growing directed network models that aim at minimizing the weighted connection expenses while at the same time favoring other important network properties such as weighted local node degrees. We employed statistical mechanics methods to study the growth of directed networks under the principle of optimizing some objective function. By mapping the system to an Ising spin model, analytic results are derived for two such models, exhibiting diverse and interesting phase transition behaviors for general edge weight, inward and outward node weight distributions. In addition, the unexplored cases of negative node weights are also investigated. Analytic results for the phase diagrams are derived showing even richer phase transition behavior, such as first-order transition due to symmetry, second-order transitions with possible reentrance, and hybrid phase transitions. We further extend previously developed zero-temperature simulation algorithm for undirected networks to the present directed case and for negative node weights, and we can obtain the minimal cost connection configuration efficiently. All the theoretical results are explicitly verified by simulations. Possible applications and implications are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=85151350651&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.107.034312

DO - 10.1103/PhysRevE.107.034312

M3 - 期刊論文

C2 - 37072985

AN - SCOPUS:85151350651

SN - 2470-0045

VL - 107

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 3

M1 - 034312

ER -