/**
* Random graph. Generates randomly k directed edges out of each node. The neighbors (edge
* targets) are chosen randomly without replacement from the nodes of the graph other than the
* source node (i.e. no loop edge is added). If k is larger than N-1 (where N is the number of
* nodes) then k is set to be N-1 and a complete graph is returned.
*
* @param g the graph to be wired
* @param k samples to be drawn for each node
* @param r source of randomness
* @return returns g for convenience
*/
public static Graph wireKOut(Graph g, int k, Random r) {
final int n = g.size();
if (n < 2) {
return g;
}
if (n <= k) {
k = n - 1;
}
int[] nodes = new int[n];
for (int i = 0; i < nodes.length; ++i) {
nodes[i] = i;
}
for (int i = 0; i < n; ++i) {
int j = 0;
while (j < k) {
int newedge = j + r.nextInt(n - j);
int tmp = nodes[j];
nodes[j] = nodes[newedge];
nodes[newedge] = tmp;
if (nodes[j] != i) {
g.setEdge(i, nodes[j]);
j++;
}
}
}
return g;
}
/**
* A sink star. Wires a sink star topology adding a link to 0 from all other nodes.
*
* @param g the graph to be wired
* @return returns g for convenience
*/
public static Graph wireStar(Graph g) {
final int n = g.size();
for (int i = 1; i < n; ++i) {
g.setEdge(i, 0);
}
return g;
}
/**
* This contains the implementation of the Barabasi-Albert model of growing scale free networks.
* The original model is described in <a href="http://arxiv.org/abs/cond-mat/0106096">
* http://arxiv.org/abs/cond-mat/0106096</a>. It also works if the graph is directed, in which
* case the model is a variation of the BA model described in <a
* href="http://arxiv.org/pdf/cond-mat/0408391">http://arxiv.org/pdf/cond-mat/0408391</a>. In both
* cases, the number of the initial set of nodes is the same as the degree parameter, and no links
* are added. The first added node is connected to all of the initial nodes, and after that the BA
* model is used normally.
*
* @param k the number of edges that are generated for each new node, also the number of initial
* nodes (that have no edges).
* @param r the randomness to be used
* @return returns g for convenience
*/
public static Graph wireScaleFreeBA(Graph g, int k, Random r) {
final int nodes = g.size();
if (nodes <= k) {
return g;
}
// edge i has ends (ends[2*i],ends[2*i+1])
int[] ends = new int[2 * k * (nodes - k)];
// Add initial edges from k to 0,1,...,k-1
for (int i = 0; i < k; i++) {
g.setEdge(k, i);
ends[2 * i] = k;
ends[2 * i + 1] = i;
}
int len = 2 * k; // edges drawn so far is len/2
for (int i = k + 1; i < nodes; i++) // over the remaining nodes
{
for (int j = 0; j < k; j++) // over the new edges
{
int target;
do {
target = ends[r.nextInt(len)];
int m = 0;
while (m < j && ends[len + 2 * m + 1] != target) {
++m;
}
if (m == j) {
break;
}
// we don't check in the graph because
// this wire method should accept graphs
// that already have edges.
} while (true);
g.setEdge(i, target);
ends[len + 2 * j] = i;
ends[len + 2 * j + 1] = target;
}
len += 2 * k;
}
return g;
}
/**
* A regular rooted tree. Wires a regular rooted tree. The root is 0, it has links to 1,...,k. In
* general, node i has links to i*k+1,...,i*k+k.
*
* @param g the graph to be wired
* @param k the number of outgoing links of nodes in the tree (except leaves that have zero
* out-links, and exactly one node that might have less than k).
* @return returns g for convenience
*/
public static Graph wireRegRootedTree(Graph g, int k) {
if (k == 0) {
return g;
}
final int n = g.size();
int i = 0; // node we wire
int j = 1; // next free node to link to
while (j < n) {
for (int l = 0; l < k && j < n; ++l, ++j) {
g.setEdge(i, j);
}
++i;
}
return g;
}
/**
* Wires a ring lattice. The added connections are defined as follows. If k is even, links to
* i-k/2, i-k/2+1, ..., i+k/2 are added (but not to i), thus adding an equal number of
* predecessors and successors. If k is odd, then we add one more successors than predecessors.
* For example, for k=4: 2 predecessors, 2 successors. For k=5: 2 predecessors, 3 successors. For
* k=1: each node is linked only to its successor. All values are understood mod n to make the
* lattice circular, where n is the number of nodes in g.
*
* @param g the graph to be wired
* @param k lattice parameter
* @return returns g for convenience
*/
public static Graph wireRingLattice(Graph g, int k) {
final int n = g.size();
int pred = k / 2;
int succ = k - pred;
for (int i = 0; i < n; ++i) {
for (int j = -pred; j <= succ; ++j) {
if (j == 0) {
continue;
}
final int v = (i + j + n) % n;
g.setEdge(i, v);
}
}
return g;
}
/**
* A hypercube. Wires a hypercube. For a node i the following links are added: i xor 2^0, i xor
* 2^1, etc. this define a log(graphsize) dimensional hypercube (if the log is an integer).
*
* @param g the graph to be wired
* @return returns g for convenience
*/
public static Graph wireHypercube(Graph g) {
final int n = g.size();
if (n <= 1) {
return g;
}
final int highestone = Integer.highestOneBit(n - 1); // not zero
for (int i = 0; i < n; ++i) {
int mask = highestone;
while (mask > 0) {
int j = i ^ mask;
if (j < n) {
g.setEdge(i, j);
}
mask = mask >> 1;
}
}
return g;
}
/**
* Watts-Strogatz model. A bit modified though: by default assumes a directed graph. This means
* that directed links are re-wired, and the undirected edges in the original (undirected) lattice
* are modeled by double directed links pointing in opposite directions. Rewiring is done with
* replacement, so the possibility of wiring two links to the same target is positive (though very
* small).
*
* <p>Note that it is possible to pass an undirected graph as a parameter. In that case the output
* is the directed graph produced by the method, converted to an undirected graph by dropping
* directionality of the edges. This graph is still not from the original undirected WS model
* though.
*
* @param g the graph to be wired
* @param k lattice parameter: this is the out-degree of a node in the ring lattice before
* rewiring
* @param p the probability of rewiring each
* @param r source of randomness
* @return returns g for convenience
*/
public static Graph wireWS(Graph g, int k, double p, Random r) {
// XXX unintuitive to call it WS due to the slight mods
final int n = g.size();
for (int i = 0; i < n; ++i) {
for (int j = -k / 2; j <= k / 2; ++j) {
if (j == 0) {
continue;
}
int newedge = (i + j + n) % n;
if (r.nextDouble() < p) {
newedge = r.nextInt(n - 1);
if (newedge >= i) {
newedge++; // random _other_ node
}
}
g.setEdge(i, newedge);
}
}
return g;
}
private boolean dfs(
final Node<Integer> node, final Node<Integer> goal, Graph<Integer> accumulator) {
try {
this.visitNode(node);
if (node.value() == goal.value()) {
return true;
}
ArrayList<Node<Integer>> stack = this.adjacencyList.get(node);
for (Node<Integer> next : stack) {
if (!this.isVisited(next) && next.value() != node.value()) {
accumulator.setNode(next.value());
accumulator.setEdge(next, node);
if (dfs(next, goal, accumulator)) {
return true;
}
}
}
return false;
} catch (NodeNotFoundException e) {
System.out.println("darf net passiern damn!");
return false;
}
}
