How group nodes if a path exists between nodes?

If I have some nodes coordinates and I have to group these nodes together if there is path exist between them. Is there any algorithm available?

The graph structure looks like below:

# Load the packages
using LightGraphs, GraphPlot, MetaGraphs, GraphRecipes, Plots
# Create a generic graph
gr = SimpleGraph()
add_vertices!(gr, size(mat_arcTwoNodes, 1))
# Add edges based on the adjacency matrix
for i in 1:size(mat_arcTwoNodes, 1), j in 1:size(mat_arcTwoNodes, 2)
    if mat_arcTwoNodes[i,j] != 0
        add_edge!(gr, i, j)
# Attach the metagraph to the original graph
mgr = MetaGraph(gr)
# Add the attribute of nodes
for i in 1:size(mat_arcTwoNodes,1)
    set_props!(mgr, i, Dict(
        Symbol("vec_xNode") => vec_xNode[i],
        Symbol("vec_yNode") => vec_yNode[i]
nodelabel = 1:nv(g)
# Plot the graph
graphplot(gr, x=vec_xNode, y=vec_yNode, names = 1:10, markersize = 2.0)

If I have co-ordinates of nodes 4,5,6,7 and 3 in the graph generated using above code. I have to group 4,5, and 6 together and 3 and 7 as another group. Is there any algorithm available for this kind of grouping?

Thanks in advance,


Check Find k-cliques in a graph

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