In a computer system comprising a plurality of components interconnected by a plurality of communications links, said plurality of components each having at least a first communications node wherein said communications nodes interface their associated component with a communications link through a node port, said nodes being capable of having a plurality of ports to which communications links to adjacent nodes couple, each node having a predetermined selection criterion established for selecting adjacent nodes coupled through its ports, said configuration of nodes and communications links comprising a directed acyclic graph wherein one node is designated a root node, all nodes coupled to only one adjacent node are designated leaf nodes, all other nodes in the graph being designated branch nodes, said acyclic directed graph having established hierarchical parent-child relations ships between all adjacent nodes proceeding from the root node down to any leaf nodes wherein a leaf node has only one parent node and all nodes adjacent to the root node are child nodes with respect to the root node but parent nodes with respect to other adjacent nodes, the root node being defined as having no parent node, a method of token passing bus access arbitration wherein a metaphorical token is passed from node to node in a cycle through the graph, the node having the token being the node with bus access, said method comprising the step of passing the token through the acyclic directed graph in an order determined by the predetermined selection criterion each node has established for selecting adjacent nodes .