Is there an wasy way to program in Tikz something like the one in the image?

It is not too difficult to draw such a thing in loops. pics may further help to avoid repetition. I did not understand your numbering scheme so you will have to modify evaluate=\Y as \Z using {int(mod(33-\Y-\X,5)+1)} to match your prescription.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{shapes.geometric,calc}
\newcounter{hexi}
\begin{document}
\begin{tikzpicture}[pics/hexi/.style={code={\stepcounter{hexi}
\node[draw,regular polygon,regular polygon sides=6,minimum width=2cm]
(hexi-\number\value{hexi}) {#1};
\foreach \Corner in {1,...,6}
{\ifodd\Corner
 \draw[fill=black] (hexi-\number\value{hexi}.corner \Corner) circle[radius=1.5pt];
\else
 \draw[fill=white] (hexi-\number\value{hexi}.corner \Corner) circle[radius=1.5pt];
\fi}
}},bullet/.style={circle,fill,inner sep=0.5pt}]
%
 \clip (0,1) rectangle (9.8,6.5);
% draw the hexagons 
 \path foreach \X in {1,...,6} {
 foreach \Y [evaluate=\Y as \Z using {int(mod(33-\Y-\X,5)+1)}] in {1,...,4} { \ifodd\X 
  ({\X*(1+cos(60))},{\Y*(2*sin(60))})
 \else
  ({\X*(1+cos(60))},{\Y*(2*sin(60))-sin(60)})
 \fi pic{hexi=\Z}}};
% draw the blue arrows
 \foreach \X in {7,9,10,11,14}
 {\foreach \Y [remember=\Y as \LastY (initially 6)]in {1,...,6}
 {\draw[blue,-latex,shorten >=2pt,shorten <=2pt] 
  ($(hexi-\X.corner \LastY)!0.1!(hexi-\X.center)$)
  -- ($(hexi-\X.corner \Y)!0.1!(hexi-\X.center)$);}}
% draw the red contour
\draw[red] ([yshift=-0.3cm]hexi-3.center) node[bullet]{}
  -- ([yshift=-0.3cm]hexi-6.center) node[bullet]{}
  -- ([yshift=-0.3cm]hexi-18.center) node[bullet]{}
  -- ([yshift=-0.3cm]hexi-16.center) node[bullet]{} -- cycle;
\end{tikzpicture}
\end{document}

Your code is far from optimal, so I'll not reproduce it here. I only show you how to add the blue arrow next to an edge, as you asked, by creating a style with arrows.

EDIT: I added also a closepath code to with arrows style in a way to be able to use it with regular polygon nodes (shown already in the @marmot's answer).

\documentclass[tikz,border=7pt]{standalone}
\usetikzlibrary{decorations.pathreplacing,calc,shapes.geometric}
\tikzstyle{with arrows}=[
    postaction={decorate,
      decoration={show path construction,
        lineto code={
          \draw [blue,-latex] ($(\tikzinputsegmentfirst)!1mm!45:(\tikzinputsegmentlast)$) -- ($(\tikzinputsegmentlast)!1mm!-45:(\tikzinputsegmentfirst)$);
        },
        closepath code={
          \draw [blue,-latex] ($(\tikzinputsegmentfirst)!1mm!45:(\tikzinputsegmentlast)$) -- ($(\tikzinputsegmentlast)!1mm!-45:(\tikzinputsegmentfirst)$);
        }
      }
    }
]
\begin{document}
  \begin{tikzpicture}
    \draw[with arrows] (0,0) -- (1,1) node[scale=2]{.} -- (2,0);
    \node[regular polygon,regular polygon sides=6,minimum width=2cm,draw,with arrows] at (3,1) {1};
  \end{tikzpicture}
\end{document}