pagination.js

str.split(',')
  .map(section => section.split(';'))
  .map(([page, rel]) => [
    Number(rxPage.exec(page)[1]),
    rxRel.exec(rel)[1]
  ]).reduce((acc, [ page, rel ]) => (
    {...acc, [rel]: page}), {}
  )

pagination2.js

const splitInSections = str => str.split(',')

const splitFields = section => section.split(';')

const formatFields = ([page, rel]) => [
  Number(rxPage.exec(page)[1]),
  rxRel.exec(rel)[1]
]

const indexing = (indexed, [page, rel]) => (
  { ...indexed, [rel]: page}
)

splitInSections(str)
  .map(splitFields)
  .map(formatFields)
  .reduce(indexing)

pagination3.js

const rxPage = /[?|&]page=(\d+)/
const rxRel = /rel="(.+)"/

const throwMustBeString = () => throw new Error('str must be a string')
const throwMustBeValid = () => throw new Error('str is a invalid string')

const isEmpty = str => str.length === 0
const isString = str => typeof str !== 'string'

const assertString = str => isString(str) ? throwMustBeString() : str
const assertValid = str => !isEmpty ? throwMustBeValid : str
const asserts = str => assertString(assertValid(str))

const splitInSections = str => str.split(',')

const splitFields = section => section.split(';')

const regexFields = ([page, rel]) => [ rxPage.exec(page), rxRel.exec(rel) ]

const mount = (indexed, [[, page], [, rel]]) => ({ ...indexed, [rel]: Number(page)})

const parser = str =>
  splitInSections(asserts(str))
    .map(splitFields)
    .map(regexFields)
    .reduce(mount)