plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected.

So far, I have figured out how to draw the dots.

My code is the following:

ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full]

I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots.

Do have any suggestions/hints on how to do that?

Thank you.

Answer

One possibility would be to use Epilog with Line:

ListPlot[
  {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, 
  Ticks -> {{1, 2, 3, 4}, None},
  AxesStyle -> Thin,
  TicksStyle -> Directive[Black, Bold, 12],
  Mesh -> Full,
  Epilog -> {
    Line[
      {{1, 1}, {2, 2}, {2, 5}, {3, 12}}

    ]
  }
]

A bit more concise:

pts = {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}};

ListPlot[
  pts, 

  Ticks -> {{1, 2, 3, 4}, None},
  AxesStyle -> Thin,
  TicksStyle -> Directive[Black, Bold, 12],
  Mesh -> Full,
  Epilog -> {
    Line[
      pts[[{1, 2, 6, 15}]]
    ]
  }
]

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