/// <summary>
/// Finds the largest clique in which nodeId is a member and returns all cliques of that size which meet that criterion.
/// </summary>
/// <param name="socialNetworkMatrix">The INetworkMatrix instance being searched.</param>
/// <param name="nodeId">The ID for the node of interest.</param>
/// <returns>The collection of ICliqueMatrix instances of maximal size which include nodeId as a member.</returns>
public static IEnumerable<ICliqueMatrix> FindLargestCliqueInvolvingNode(INetworkMatrix socialNetworkMatrix, int nodeId)
{
var relatedNodes = new List<int>(Enumerable.Range(1, socialNetworkMatrix.NodeCount).Where<int>( secondNodeId => socialNetworkMatrix.NodesRelate(nodeId, secondNodeId) ));
var tuple = CreateSubnetworkFromNodeIds(socialNetworkMatrix, relatedNodes);
var subnetwork = tuple.Item1;
var map = tuple.Item2;
var inverseMap = tuple.Item3;
// uses the smaller subnetwork created from the related nodes of nodeId to search for a clique of maximal size,
// of which we are guaranteed that nodeId is a member (since it is related to all nodes in this subnetwork)
//
// in turn, this collection of maximal cliques is mapped back to a collection of ICliqueMatrix instances where
// the node IDs reflect the node IDs of the original socialNetworkMatrix
return FindLargestClique(subnetwork)
.Select<ICliqueMatrix, ICliqueMatrix>(
cliqueOfSubnet => NetworkMatrixFactory.CreateCliqueMatrix( cliqueOfSubnet.MemberNodeIds.Select<int, int>( subnetId => inverseMap[subnetId] ), socialNetworkMatrix.NodeCount) );
}
