Align caption text to center and have its label to the left

Question

I am trying to have the caption of a figure aligned as it is below:

Description: I included a few rows of text above and below the figure to see the alignment of the caption. It seems to me that the text of the caption is aligned to center while the label Fig. 1.1.1. is somehow floating at the lest of the text.

Here's what I tried:

\begin{figure}
    \centering\captionsetup{format = hang}

    \includegraphics[width=7cm]{assets/basic}
    \caption{Some long caption here}
    \label{fig:my_label}
\end{figure}

The multiple rows in the caption are correctly justified under the first, but the entire caption box is then aligned to the left.

How can I achieve that effect, please?

EDIT

I have created an example document to illustrate my problem:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{graphicx, caption, threeparttable}
\usepackage{floatrow}

\title{FigureCaption}
\author{Victor Barbu}

\begin{document}

\section{Testing Captions}

\begin{figure}[h]
    \centering\captionsetup{format = hang}

    \includegraphics[width=7cm]{pic}
    \caption{The graph on $V = \{1,\ldots,7\}$ with edge set\\ $E = \{(1,2),(1,5),(2,5),(3,4),(5,7)\}$}
    \label{fig:my_label}
\end{figure}


\end{document}

Answer 1

as far as i understood your question you looking for something like this:

but i might be wrong :-(

\documentclass{article}
%\usepackage[utf8]{inputenc}
%\usepackage{amsmath}
\usepackage[demo]{graphicx}
%\usepackage{threeparttable}
\usepackage{caption}

%\title{FigureCaption}
%\author{Victor Barbu}

\begin{document}

%\section{Testing Captions}

\begin{figure}[h]
    \centering\captionsetup{format = hang, width=8cm}
    \includegraphics[width=7cm]{pic}
    \caption{The graph on $V = \{1,\ldots,7\}$ with edge set $E = \{(1,2),(1,5),(2,5),(3,4),(5,7)\}$}
    \label{fig:my_label}
\end{figure}
\end{document}