function Graph(opts) {
  this._isDirected = _.has(opts, "directed") ? opts.directed : true;
  this._isMultigraph = _.has(opts, "multigraph") ? opts.multigraph : false;
  this._isCompound = _.has(opts, "compound") ? opts.compound : false;

  // Label for the graph itself
  this._label = undefined;

  // Defaults to be set when creating a new node
  this._defaultNodeLabelFn = _.constant(undefined);

  // Defaults to be set when creating a new edge
  this._defaultEdgeLabelFn = _.constant(undefined);

  // v -> label
  this._nodes = {};

  if (this._isCompound) {
    // v -> parent
    this._parent = {};

    // v -> children
    this._children = {};
    this._children[GRAPH_NODE] = {};
  }

  // v -> edgeObj
  this._in = {};

  // u -> v -> Number
  this._preds = {};

  // v -> edgeObj
  this._out = {};

  // v -> w -> Number
  this._sucs = {};

  // e -> edgeObj
  this._edgeObjs = {};

  // e -> label
  this._edgeLabels = {};
}
Decreases the priority for **key** to **priority**. If the new priority is
greater than the previous priority, this function will throw an Error.

@param {Object} key the key for which to raise priority
@param {Number} priority the new priority for the key