Description Usage Arguments Details Value Examples

This is a collection of functions computing the distance between two networks.

1 2 3 4 5 6 7 | ```
dist_hamming(x, y, representation = "laplacian")
dist_frobenius(x, y, representation = "laplacian")
dist_spectral(x, y, representation = "laplacian")
dist_root_euclidean(x, y, representation = "laplacian")
``` |

`x` |
An |

`y` |
An |

`representation` |
A string specifying the desired type of representation,
among: |

Let *X* be the matrix representation of network *x* and *Y* be
the matrix representation of network *y*. The Hamming distance between
*x* and *y* is given by

*\frac{1}{N(N-1)} ∑_{i,j} |X_{ij} -
Y_{ij}|,*

where *N* is the number of vertices in networks *x* and
*y*. The Frobenius distance between *x* and *y* is given by

*√{∑_{i,j} (X_{ij} - Y_{ij})^2}.*

The spectral distance between
*x* and *y* is given by

*√{∑_i (a_i - b_i)^2},*

where
*a* and *b* of the eigenvalues of *X* and *Y*, respectively.
This distance gives rise to classes of equivalence. Consider the spectral
decomposition of *X* and *Y*:

*X=VAV^{-1}*

and

*Y =
UBU^{-1},*

where *V* and *U* are the matrices whose colums are the
eigenvectors of *X* and *Y*, respectively and *A* and *B* are
the diagonal matrices with elements the eigenvalues of *X* and *Y*,
respectively. The root-Euclidean distance between *x* and *y* is
given by

*√{∑_i (V √{A} V^{-1} - U √{B} U^{-1})^2}.*

Root-Euclidean distance can used only with the laplacian matrix representation.

A scalar measuring the distance between the two input networks.

1 2 3 4 5 6 | ```
g1 <- igraph::sample_gnp(20, 0.1)
g2 <- igraph::sample_gnp(20, 0.2)
dist_hamming(g1, g2, "adjacency")
dist_frobenius(g1, g2, "adjacency")
dist_spectral(g1, g2, "laplacian")
dist_root_euclidean(g1, g2, "laplacian")
``` |

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