# Computing the Line Index of Balance Using Integer Programming Optimisation

@article{Aref2017ComputingTL, title={Computing the Line Index of Balance Using Integer Programming Optimisation}, author={S. Aref and A. Mason and M. Wilson}, journal={ArXiv}, year={2017}, volume={abs/1710.09876} }

An important measure of signed graphs is the line index of balance which has applications in many fields. However, this graph-theoretic measure was underused for decades because of the inherent complexity in its computation which is closely related to solving NP-hard graph optimisation problems like MAXCUT. We develop new quadratic and linear programming models to compute the line index of balance exactly. Using the Gurobi integer programming optimisation solver, we evaluate the line index of… CONTINUE READING

#### Figures, Tables, and Topics from this paper

9 Citations

A modeling and computational study of the frustration index in signed networks

- Computer Science, Physics
- Networks
- 2020

5

Signed Network Structural Analysis and Applications with a Focus on Balance Theory

- Computer Science, Mathematics
- ArXiv
- 2019

1- PDF

Balance and Frustration in Signed Networks under Different Contexts

- Computer Science, Psychology
- J. Complex Networks
- 2019

14- PDF

The Many Faces of Balance: Multilevel Structural Evaluation of Signed Directed Social Networks

- Computer Science
- ArXiv
- 2020

Multilevel structural evaluation of signed directed social networks based on balance theory

- Computer Science, Medicine
- Scientific reports
- 2020

- PDF

Legislative effectiveness hangs in the balance: Studying balance and polarization through partitioning signed networks

- Political Science, Computer Science
- ArXiv
- 2019

1

Detecting coalitions by optimally partitioning signed networks of political collaboration

- Computer Science, Mathematics
- Scientific Reports
- 2020

4- PDF

#### References

SHOWING 1-10 OF 76 REFERENCES

An exact method for computing the frustration index in signed networks using binary programming

- Computer Science, Mathematics
- ArXiv
- 2016

13- PDF

Separator-based data reduction for signed graph balancing

- Computer Science, Mathematics
- J. Comb. Optim.
- 2010

42 Highly Influential- PDF

Algorithmic and complexity results for decompositions of biological networks into monotone subsystems

- Mathematics, Computer Science
- Biosyst.
- 2007

66- PDF

A memetic algorithm for computing and transforming structural balance in signed networks

- Computer Science
- Knowl. Based Syst.
- 2015

28

Studies on the balancing, the minimal balancing, and the minimum balancing processes for social groups with planar and nonplanar graph structures

- Mathematics
- 1978

39

Balance and Frustration in Signed Networks under Different Contexts

- Computer Science, Psychology
- J. Complex Networks
- 2019

14- PDF

Applications of Structural Balance in Signed Social Networks

- Mathematics, Computer Science
- ArXiv
- 2014

21- PDF

Fixed-Parameter Algorithms in Analysis of Heuristics for Extracting Networks in Linear Programs

- Mathematics, Computer Science
- IWPEC
- 2009

8