Abstract: A network topology system having a plurality of nodes for data exchange is provided, with the number of said nodes being N. The nodes are sequentially connected to form a ring communication configuration. N is an even integer. The i-th node of said nodes connects to the [(i+m) mod N]-th and [(i+p) mod N]-th nodes according to a connection rule. The j-th node of said nodes connects to the [(j?m) mod N]-th and [(j+p) mod N]-th nodes according to the connection rule. i and j are non-negative integers and are less than N. m and p are integers and not larger than N. Here, i and m are odd numbers, and j and p are even numbers.

Abstract: A network topology system having a plurality of nodes for data exchange is provided, with the number of said nodes being N. The nodes are sequentially connected to form a ring communication configuration. N is an even integer. The i-th node of said nodes connects to the [(i+m) mod N]-th and [(i+p) mod N]-th nodes according to a connection rule. The j-th node of said nodes connects to the [(j?m) mod N]-th and [(j+p) mod N]-th nodes according to the connection rule. i and j are non-negative integers and are less than N. m and p are integers and not larger than N. Here, i and m are odd numbers, and j and p are even numbers.

Abstract: A network topology system comprises a plurality of nodes, each of the plurality of nodes having a set of connection rules which is built by the steps of: generating a series of prime number differences; generating a series of communication strategy numbers; extracting as many terms as the number of connecting nodes from a recursive sequences to serve as an index series; generating a series of connection strategy numbers by extracting the Nth terms from the series of communication strategy numbers, wherein N stands for each number of the index series; and generating a series of connecting nodes numbers by calculating the sum of each odd number and each term of the series of connection strategy numbers so as to build the connection rules for each odd-numbered node to connect the nodes numbered in corresponding with the numbers of the connecting nodes number series.

Abstract: A network topology system comprises a plurality of nodes, each of the plurality of nodes having a set of connection rules which is built by the steps of: generating a series of prime number differences; generating a series of communication strategy numbers; extracting as many terms as the number of connecting nodes from a recursive sequences to serve as an index series; generating a series of connection strategy numbers by extracting the Nth terms from the series of communication strategy numbers, wherein N stands for each number of the index series; and generating a series of connecting nodes numbers by calculating the sum of each odd number and each term of the series of connection strategy numbers so as to build the connection rules for each odd-numbered node to connect the nodes numbered in corresponding with the numbers of the connecting nodes number series.

Abstract: A switchless network topology system for parallel computation is provided. The switchless network topology system includes a plurality of nodes, of which one node communicates with another node according to a routing table, where the creation of the routing table includes the following steps: calculating a shortest path of transmission paths between two nodes of the nodes, where the shortest path has no relay node or at least one relay node between the two nodes; removing the transmission path between a starting node and a first relay node of the shortest path and identifying another shortest path between the starting node and the destination node; repeating the step of removing and identifying to identify other shortest paths between the starting node and the destination node; and creating the routing table based on every shortest path between any starting node and any destination node of the nodes.

Abstract: A switchless network topology system for parallel computation is provided. The switchless network topology system includes a plurality of nodes, of which one node communicates with another node according to a routing table, where the creation of the routing table includes the following steps: calculating a shortest path of transmission paths between two nodes of the nodes, where the shortest path has no relay node or at least one relay node between the two nodes; removing the transmission path between a starting node and a first relay node of the shortest path and identifying another shortest path between the starting node and the destination node; repeating the step of removing and identifying to identify other shortest paths between the starting node and the destination node; and creating the routing table based on every shortest path between any starting node and any destination node of the nodes.