Shock back-to-back defeats for Manchester City over Christmas have coincided with the absence of Fernandinho, who seems to be truly irreplaceable in Pep Guardiola's side.

Guardiola has international players competing for places all over the pitch, but there is nobody who has yet shown they can do what the Brazil midfielder does. Both John Stones and Ilkay Gundogan have tried, but City just are not the same team without Fernandinho's mix of ball-winning and passing.

Here Press Association Sport looks at who might be irreplaceable for the other sides in the Premier League's top six.

Liverpool – Virgil Van Dijk

Defence was Liverpool's Achilles heel until the arrival of Virgil Van Dijk in a £75million deal from Southampton last winter. At the time Liverpool were accused of overpaying for the Dutchman, but they would happily sign that cheque again given the impact he has had at Anfield. The 4-0 Boxing Day win over Newcastle was Van Dijk's 33rd league game for Liverpool, and the 19th clean sheet he has been part of keeping. Liverpool beat Manchester City to the signing of Van Dijk, with City feeling he was overpriced and turning instead to Aymeric Laporte. However, Premier League statistics show Liverpool have got more for their money in just about every department, with Van Dijk ranking ahead of the Frenchman in blocks, interceptions, tackles, clearances and aerial battles won – and crucially in terms of goals conceded and clean sheets.

Tottenham – Harry Kane

Harry Kane's strike in the 5-0 Boxing Day win over Bournemouth took the England captain to 17 goals for Spurs this season in 31 appearances – and to 120 goals in 172 Premier League appearances. Those remarkable numbers show why Kane is an automatic starter, but also why he is so hard to replace. The only like-for-like replacements in Tottenham's squad have never convinced – Fernando Llorente has not scored in four substitute appearances this season while Vincent Janssen is yet to feature at all. The only league game this season that Kane did not start, away to Leicester, saw Son Heung-min moved inside but it is not their most effective shape.

Chelsea – Eden Hazard

Eden Hazard became the 10th player to reach 100 competitive goals for Chelsea on Boxing Day when his brace in the 2-1 win at Watford took him to 101 for the club. He has now been directly involved in 19 Premier League goals this season – scoring 10 and creating nine – which is more than any other player. After the game Hazard spoke about his desire to stay with the Blues and win more trophies – which will come as welcome news to Chelsea fans given the constant speculation linking the Belgium star with Real Madrid.

Arsenal – Pierre-Emerick Aubameyang

Pierre-Emerick Aubameyang has made a huge impact at Arsenal since arriving almost a year ago. His goal against Brighton on Boxing Day took him to 13 in the Premier League for the season – almost one third of Arsenal's total as a team – and ensured he remained atop the division's scoring charts at the mid-point of the campaign. That scoring record has continued despite the occasions on which he has found himself shunted out to the left to accommodate Alexandre Lacazette in Unai Emery's system, and his goals are surely vital to Arsenal's continued pursuit of a return to the Champions League.

Manchester United – David De Gea

David De Gea's importance to Manchester United has been clear for some time, but he demonstrated it again on Wednesday. A 3-1 win over Huddersfield continued Ole Gunnar Solskjaer's honeymoon period following his return as interim manager. However, it could have all been very different but for De Gea's outstanding save  to deny Laurent Depoitre with United's lead still at 1-0. The Spaniard ranks fourth in the Premier League this season having made 64 saves, and it is no surprise that all those goalkeepers above him (and those immediately below) play for clubs who are, or in West Ham's case were initially, at the wrong end of the table. Jose Mourinho constantly chopped and changed his team, unhappy with their performances, but there was never any question of who would play in goal. If United are able to rescue a top-four spot over the second half of the campaign, their goalkeeper will be a huge part of the reason why.