TY - JOUR

T1 - Quantum walk inspired algorithm for graph similarity and isomorphism

AU - Schofield, Callum

AU - Wang, Jingbo B.

AU - Li, Yuying

PY - 2020/8/1

Y1 - 2020/8/1

N2 - Large-scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modelled using network graphs. Valuable insight can be gained by measuring similarity between network graphs in order to make quantitative comparisons. Since these networks can be very large, scalability and efficiency of the algorithm are key concerns. More importantly, for graphs with unknown labelling, this graph similarity problem requires exponential time to solve using existing algorithms. In this paper, we propose a quantum walk inspired algorithm, which provides a solution to the graph similarity problem without prior knowledge on graph labelling. This algorithm is capable of distinguishing between minor structural differences, such as between strongly regular graphs with the same parameters. The algorithm has a polynomial complexity, scaling with O(n9).

AB - Large-scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modelled using network graphs. Valuable insight can be gained by measuring similarity between network graphs in order to make quantitative comparisons. Since these networks can be very large, scalability and efficiency of the algorithm are key concerns. More importantly, for graphs with unknown labelling, this graph similarity problem requires exponential time to solve using existing algorithms. In this paper, we propose a quantum walk inspired algorithm, which provides a solution to the graph similarity problem without prior knowledge on graph labelling. This algorithm is capable of distinguishing between minor structural differences, such as between strongly regular graphs with the same parameters. The algorithm has a polynomial complexity, scaling with O(n9).

KW - Graph isomorphism

KW - Graph similarity

KW - Quantum inspired algorithms

KW - Quantum walks

UR - http://www.scopus.com/inward/record.url?scp=85089731422&partnerID=8YFLogxK

U2 - 10.1007/s11128-020-02758-7

DO - 10.1007/s11128-020-02758-7

M3 - Article

AN - SCOPUS:85089731422

VL - 19

JO - Quantum Information Processing

JF - Quantum Information Processing

SN - 1570-0755

IS - 9

M1 - 281

ER -