  A social group is represented by a graph, where each pair of nodes is
connected by two oppositely directed links. At the beginning, a given amount
$p(i)$ of resources is assigned randomly to each node $i$. Also, each link
$r(i,j)$ is initially represented by a random positive value, which means the
percentage of resources of node $i$ which is offered to node $j$. Initially
then, the graph is fully connected, i.e. all non-diagonal matrix elements
$r(i,j)$ are different from zero. During the simulation, the amounts of
resources $p(i)$ change according to the balance equation. Also, nodes
reorganise their activity with time, going to give more resources to those
which give them more. This is the rule of varying the coefficients $r(i,j)$.
The result is that after some transient time, only some pairs $(m,n)$ of nodes
survive with non-zero $p(m)$ and $p(n)$, each pair with symmetric and positive
$r(m,n)=r(n,m)$. Other coefficients $r(m,i\ne n)$ vanish. Unpaired nodes remain
with no resources, i.e. their $p(i)=0$, and they cease to be active, as they
have nothing to offer. The percentage of survivors (i.e. those with with $p(i)$
positive) increases with the velocity of varying the numbers $r(i,j)$, and it
slightly decreases with the size of the group. The picture and the results can
be interpreted as a description of a social algorithm leading to marriages.
