An outstanding display from Phil Foden led the Premier League champions to a comfortable victory in the south coast, with the Stockport-born star grabbing a brace
Guardiola's men have now avoided defeat in their previous eight league outings, winning six and drawing two, which has seen them jump to second place in the table ahead of Liverpool's clash Manchester United on Sunday.
Having well and truly recovered from a shaky start to the season, City are in a rich vein of form with three wins in three ahead of their Carabao Cup tie away at West Ham on Wednesday evening.
Following the win, Guardiola raved about the competitive nature of the Premier League, which the Spanish boss has often tagged as the strongest league in world football.
"Many top clubs. That's why it (Premier League) is the best league in the world. Be proud to live these years in your country. It's a privilege," said Guardiola in his post-match interview.
"It's my sixth season (in England), every season is stronger than the year before. Top managers, look at Graham (Potter). The clubs, teams, every manager the sense."
Guardiola is aiming for his fourth league title since arriving to City in 2016. The 50-year-old added: "Arsenal are growing, one game a week, and they will be there, Chelsea of course, Liverpool, (Manchester) United.
"(The other managers) make me better, that's for sure. I tell you how many times thinking how to handle Liverpool and with Thomas Tuchel again, and every time against Mikel (Arteta), this game (against Brighton).
"Every manager has this trick to make you think how to beat them. After you win, I'm congratulated, and after you lose congratulate them."
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