I want to create a plot showing connections between nodes from an adjacency matrix like the one below.
As of R2015b, MATLAB now has a suite of graph and network algorithms. For this example, you can create an undirected graph object and then plot it using the overloaded plot function:
% Create symmetric adjacency matrix
A = [1 1 0 0 1 0;
1 0 1 0 1 0;
0 1 0 1 0 0;
0 0 1 0 1 1;
1 1 0 1 0 0;
0 0 0 1 0 0];
% Create undirected graph object
G = graph(A);
% Plot
plot(G);