Hi Victoria,

This reply is likely 6 years too late.  But I recently asked the exact same question.  Since I couldn't find anyone else who had done the work, I decided to write it based on Robert's suggestion.  Here is what I wrote.  Hopefully, it will be helpful to someone else.

To use it, just put in an adjacency matrix and specify pathlength (i.e. 3).  You should get a vector back of all of the possible paths.  For me, I wasn't interested in paths where you back track and visit a node more than once, so I included a backtrack flag to specify where you care about back tracking or not.

HTH,

Ken

=== code ===

findPath <- function(adj.matrix, pathlengths, backtrack=F, plot=F){
    if(plot){
        require(Rgraphviz)
        testgraph <- new("graphAM", adj.matrix, edgemode="directed")
        plot(testgraph, attrs=list(node =list(fillcolor="lightblue"), edge=list(arrowsize=0.5)))
    }
    
    converted.path.matrix <- matrix("", nrow=nrow(adj.matrix), ncol=ncol(adj.matrix))
    path.matrix <- matrix("", nrow=nrow(adj.matrix), ncol=ncol(adj.matrix))
    for (i in 1:nrow(adj.matrix)){
        for (j in 1:ncol(adj.matrix)){
            if (adj.matrix[i,j] == 1) {
                converted.path.matrix[i,j] <- paste(c(i,j), collapse=",")
                path.matrix[i,j] <- j
            }
        }
    }
    
    new.path.matrix = converted.path.matrix
    
    if (pathlengths == 1)
        return(as.vector(return_paths(new.path.matrix, backtrack)))    
    if (pathlengths > 1){
        for (n in 2:pathlengths){
            new.path.matrix <- matrix_combine(new.path.matrix, path.matrix)
        }
    }
    return(as.vector(return_paths(new.path.matrix, backtrack)))
}

# A and B both matrix
matrix_combine <- function(A, B){
    #data checks
    if (!is.matrix(A) | !is.matrix(B))
        stop ("A needs to be a matrix, B needs to be a matrix")
    if (ncol(A) != nrow(B) | nrow(A) != ncol(B))
        stop ("Incompatible matrix dimensions between A and B!")
    
    result <- matrix("", nrow=nrow(A), ncol=ncol(B))
    for (i in 1:ncol(A)){
        #print(paste("i=", i))
        for (j in 1:nrow(A)){
            #print(paste("j=", j))
            temp <- NULL
            for (k in 1:ncol(A)){
                #print(paste("k=", k))
                temp <- c(temp, combine_paths(A[i,k], B[k,j]))   
            }
            temp2 <- lapply(temp, function(x){
                junk <- NULL
                if (x != ""){
                    junk <- c(junk, x)
                }
                junk
            })
            temp2 <- paste(unlist(temp2), collapse="/")
            result[i,j] <- temp2
        }
    }
    result
}

combine_paths <- function(x,y){
    result <- ""
    counter <- 1
    for (i in unlist(strsplit(as.character(x), split="/"))) {
        for (j in y){
            if (i != "" & j != "" & counter != 1){
                result <- c(result, paste(c(i,j), collapse=","))
            } else if (i != "" & j != "" & counter == 1){
                result <- paste(c(i,j), collapse=",")
            }
            counter = counter + 1
        }
    }
    if (length(result) > 1) return(paste(result, collapse="/"))
    return(result)
}

return_paths <- function(path.matrix, backtrack=F){
    result <- NULL
    if (is.matrix(path.matrix)){
        for (i in 1:nrow(path.matrix)){
            for (j in 1:ncol(path.matrix)){
                if (path.matrix[i,j] != ""){
                    result <- c(result, strsplit(path.matrix[i,j], split="/"))
                }
            }
        }
    } 
    result <- unique(sort(unlist(result)))
    if (!backtrack) {
        unlist(sapply(result, function(x){
            temp <- unlist(strsplit(x, split=","))
            if( length(unique(temp)) != length(temp)) return(NULL)
            x
        }))
    } else {
        result
    }
}