Table 2 Competitor Distance Scores & Our Metrics

(Non-metric) Distance Score Algorithms

NetAlignBP

Network Alignment using Belief Propagation (Bayati et al. 2009)

IsoRank

Neighborhood Topology Isomorphism using Page Rank (Singh et al. 2007)

SparseIsoRank

Neighborhood Topology Sparse Isomorphism using Page Rank (Bayati et al. 2009)

InnerPerm

Inner Product Matching with Permutations (Lyzinski et al. 2016)

InnerDSL1

Inner Product Matching with Matrices in \(\mathbb {W}^{n}\) and entry-wise 1-norm (Lyzinski et al. 2016)

InnerDSL2

Inner Product Matching with Matrices in \(\mathbb {W}^{n}\) and Frobenius norm (Lyzinski et al. 2016)

NetAlignMR

Iterative Matching Relaxation (Klau 2009)

Natalie (V2.0)

Improved Iterative Matching Relaxation (El-Kebir et al. 2015)

Metrics from our Family (2)

EXACT

Chemical Distance via brute force search over GPU

DSL1

Doubly Stochastic Chemical Distance \(d_{\mathbb {W}^{n}}\) with entry-wise 1-norm

DSL2

Doubly Stochastic Chemical Distance \(d_{\mathbb {W}^{n}}\) with Frobenius norm

ORTHOP

Orthogonal Relaxation of Chemical Distance \(d_{\mathbb {O}^{n}}\) with operator 2-norm

ORTHFR

Orthogonal Relaxation of Chemical Distance \(d_{\mathbb {O}^{n}}\) with Frobenius norm