/****************
Edge EdgeTree2EdgeList
Write the edgelist of a network into tail and head arrays.
Returns the number of edges in the network.
****************/
Edge EdgeTree2EdgeList(Vertex *tails, Vertex *heads, Network *nwp, Edge nmax){
Edge nextedge=0;
/* *** don't forget, tail -> head */
if (nwp->directed_flag) {
for (Vertex v=1; v<=nwp->nnodes; v++){
for(Vertex e = EdgetreeMinimum(nwp->outedges, v);
nwp->outedges[e].value != 0 && nextedge < nmax;
e = EdgetreeSuccessor(nwp->outedges, e)){
tails[nextedge] = v;
heads[nextedge] = nwp->outedges[e].value;
nextedge++;
}
}
}else{
for (Vertex v=1; v<=nwp->nnodes; v++){
for(Vertex e = EdgetreeMinimum(nwp->outedges, v);
nwp->outedges[e].value != 0 && nextedge < nmax;
e = EdgetreeSuccessor(nwp->outedges, e)){
Vertex k = nwp->outedges[e].value;
if(v < k){
tails[nextedge] = k;
heads[nextedge] = v;
nextedge++;
}else{
tails[nextedge] = v;
heads[nextedge] = k;
nextedge++;
}
}
}
}
return nextedge;
}
int FindithEdge (Vertex *tail, Vertex *head, Edge i, Network *nwp) {
Vertex taili=1;
Edge e;
/* TODO: This could be speeded up by a factor of 3 or more by starting
the search from the tail n rather than tail 1 if i > ndyads/2. */
if (i > nwp->nedges || i<=0)
return 0;
while (i > nwp->outdegree[taili]) {
i -= nwp->outdegree[taili];
taili++;
}
/* TODO: This could be speeded up by a factor of 3 or more by starting
the search from the tree maximum rather than minimum (left over) i > outdegree[taili]. */
e=EdgetreeMinimum(nwp->outedges,taili);
while (i-- > 1) {
e=EdgetreeSuccessor(nwp->outedges, e);
}
*tail = taili;
*head = nwp->outedges[e].value;
return 1;
}
int FindithNonedge (Vertex *tail, Vertex *head, Edge i, Network *nwp) {
Vertex taili=1;
Edge e;
Edge ndyads = DYADCOUNT(nwp->nnodes, nwp->bipartite, nwp->directed_flag);
// If the index is too high or too low, exit immediately.
if (i > ndyads - nwp->nedges || i<=0)
return 0;
/* TODO: This could be speeded up by a factor of 3 or more by starting
the search from the tail n rather than tail 1 if i > ndyads/2. */
Vertex nnt;
while (i > (nnt = nwp->nnodes - (nwp->bipartite ? nwp->bipartite : (nwp->directed_flag?1:taili))
- nwp->outdegree[taili])) { // nnt is the number of nonties incident on taili. Note that when network is undirected, tail<head.
i -= nnt;
taili++;
}
// Now, our tail is taili.
/* TODO: This could be speeded up by a factor of 3 or more by starting
the search from the tree maximum rather than minimum (left over) i > outdegree[taili]. */
// If taili 1, then head cannot be 1. If undirected, the smallest it can be is taili+1. If bipartite, the smallest it can be is nwp->bipartite+1.
Vertex lhead = (
nwp->bipartite ?
nwp->bipartite :
(nwp->directed_flag ?
taili==1 : taili)
);
e = EdgetreeMinimum(nwp->outedges,taili);
Vertex rhead = nwp->outedges[e].value;
// Note that rhead-lhead-1-(lhead<taili && taili<rhead) is the number of nonties between two successive ties.
// the -(lhead<taili && taili<rhead) is because (taili,taili) is not a valid nontie and must be skipped.
// Note that if taili is an isolate, rhead will be 0.
while (rhead && i > rhead-lhead-1-(lhead<taili && taili<rhead)) {
i -= rhead-lhead-1-(lhead<taili && taili<rhead);
lhead = rhead;
e = EdgetreeSuccessor(nwp->outedges, e);
// If rhead was the highest-indexed head, then e is now 0.
if(e) rhead = nwp->outedges[e].value;
else break; // Note that we don't actually need rhead in the final step.
}
// Now, the head we are looking for is (left over) i after lhead.
*tail = taili;
*head = lhead + i + (nwp->directed_flag && lhead+i>=taili); // Skip over the (taili,taili) dyad, if the network is directed.
return 1;
}
/*****************
int DeleteHalfedgeFromTree
Delete the TreeNode with value b from the tree rooted at edges[a].
Return 0 if no such TreeNode exists, 1 otherwise. Also update the
value of *last_edge appropriately.
*****************/
int DeleteHalfedgeFromTree(Vertex a, Vertex b, TreeNode *edges,
Edge *last_edge){
Edge x, z, root=(Edge)a;
TreeNode *xptr, *zptr, *ptr;
if ((z=EdgetreeSearch(a, b, edges))==0) /* z is the current TreeNode. */
return 0; /* This edge doesn't exist, so return 0 */
/* First, determine which node to splice out; this is z. If the current
z has two children, then we'll actually splice out its successor. */
if ((zptr=edges+z)->left != 0 && zptr->right != 0) {
if(unif_rand()<0.5)
z=EdgetreeSuccessor(edges, z);
else
z=EdgetreePredecessor(edges, z);
zptr->value = (ptr=edges+z)->value;
zptr=ptr;
}
/* Set x to the child of z (there is at most one). */
if ((x=zptr->left) == 0)
x = zptr->right;
/* Splice out node z */
if (z == root) {
zptr->value = (xptr=edges+x)->value;
if (x != 0) {
if ((zptr->left=xptr->left) != 0)
(edges+zptr->left)->parent = z;
if ((zptr->right=xptr->right) != 0)
(edges+zptr->right)->parent = z;
zptr=edges+(z=x);
} else
return 1;
} else {
if (x != 0)
(xptr=edges+x)->parent = zptr->parent;
if (z==(ptr=(edges+zptr->parent))->left)
ptr->left = x;
else
ptr->right = x;
}
/* Clear z node, update *last_edge if necessary. */
zptr->value=0;
if(z!=root){
RelocateHalfedge(*last_edge,z,edges);
(*last_edge)--;
}
return 1;
}
/*********************
void MH_BipartiteCondDegreeDist
Pick three nodes -- tail, head, alter -- such that
* tail shares an edge with head
* tail does not share an edge with A
* deg(head) = deg(A) + 1
Then, propose swapping the (tail,head) edge for a (tail,A) edge so that
deg(tail) stays the same while deg(head) and deg(A) swap
with one another.
*********************/
void MH_BipartiteCondDegreeDist (MHproposal *MHp, Network *nwp) {
int valid, count;
Edge e;
Vertex tail, head, A, tailin, tailout, headdeg, Adeg, minA, maxA, i, k;
double u;
TreeNode *tail_edges;
Vertex *headA_degrees;
/* *** don't forget, edges are (tail, head) now */
if(MHp->ntoggles == 0) { /* Initialize */
MHp->ntoggles=2;
return;
}
MHp->logratio += 0; /* By symmetry: P(choosing tail,head,A) must equal */
/* P(choosing tail,A,head after head and A swap roles), */
/* which makes the ratio equal to 1. */
for(valid = count = 0; valid == 0 && count<MAX_TRIES/10; count++) {
tailin = tailout = 0;
/* choose a node at random; ensure it has some edges */
while (tailin + tailout == 0) {
u = unif_rand();
if (u < .5) { /* Pick "male" and "female" nodes with equal prob */
tail = 1 + unif_rand() * nwp->bipartite;
} else {
tail = 1 + nwp->bipartite + unif_rand() * (nwp->nnodes - nwp->bipartite);
}
tailin = nwp->indegree[tail];
tailout = nwp->outdegree[tail];
}
/* select an edge to/from tail at random */
k = (int)(unif_rand() * (tailout + tailin));
if (k < tailout) { /* we chose an outedge */
tail_edges = nwp->outedges;
i = k;
headA_degrees = nwp->indegree;
} else { /* we chose an inedge */
tail_edges = nwp->inedges;
i = k - tailout;
headA_degrees = nwp->outdegree;
}
/* Find ith edge in correct edgetree for tail; this will be (tail,head) or (head,tail) */
e=EdgetreeMinimum(tail_edges, tail);
while (i-- > 0) {
e=EdgetreeSuccessor(tail_edges, e);
}
head = tail_edges[e].value;
headdeg = nwp->directed_flag ? headA_degrees[head] : nwp->indegree[head] + nwp->outdegree[head];
/* Now choose alter at random */
/* Now search for eligible alters */
minA = (u<.5) ? 1 + nwp->bipartite : 1 ;
maxA = (u<.5) ? nwp->nnodes : nwp->bipartite;
i=0;
for (A=minA; A<=maxA; A++) {
Adeg = nwp->directed_flag ? headA_degrees[A] : nwp->indegree[A] + nwp->outdegree[A];
/* To be a valid choice, alter (A) must not be tied to tail and it must have */
/* a degree one less than the head */
if (headdeg == Adeg + 1 && EdgetreeSearch(tail, A, tail_edges) == 0) {
if (nwp->directed_flag || EdgetreeSearch(A, tail, tail_edges) ==0) {
i++;
}
}
} /* After for-loop, i is # of eligible alters. */
if (i>0) {
valid = 1;
i = 1 + unif_rand()*i; /* Pick an eligible alter at random */
for (A=minA; i>0; A++) {
Adeg = nwp->directed_flag ? headA_degrees[A] : nwp->indegree[A] + nwp->outdegree[A];
/* To be a valid choice, alter (A) must not be tied to tail and it must have */
/* a degree one less than the head */
if (headdeg == Adeg + 1 && EdgetreeSearch(tail, A, tail_edges) == 0) {
if (nwp->directed_flag || EdgetreeSearch(A, tail, tail_edges) ==0) {
i--; /* By counting down, when i==0 we have the selected A. */
}
}
}
}
}
if ( (!nwp->directed_flag && tail > head) ||
(nwp->directed_flag && k < tailout) )
{
Mtail[0] = head;
Mhead[0] = tail;
}else{
Mtail[0] = tail;
Mhead[0] = head;
}
if(!valid) {
Mtail[1] = Mtail[0];
Mhead[1] = Mtail[0];
} else {
if ( (!nwp->directed_flag && tail > A) ||
(nwp->directed_flag && k < tailout) )
{
Mtail[0] = A;
Mhead[0] = tail;
}else{
Mtail[0] = tail;
Mhead[0] = A;
}
}
}