Global cities alpha beta gamma10/15/2023 ![]() ![]() This number ( u) is estimated through the number of nodes ( v), links ( e) and of sub-graphs ( p). The maximum number of independent cycles in a graph. Planar networks often have a large diameter due to many intermediate stops between two distant nodes. Graphs whose extent remains constant, but with higher connectivity, have lower diameter values. In the case of a complex graph, the diameter can be found with a topological distance matrix (Shimbel distance), which computes for each node pair its minimal topological distance. A high diameter implies a less linked network. The diameter enables us to measure the development of a network in time. ![]() It measures the extent of a graph and the topological length between two nodes. ![]() The length of the shortest path between the most distanced nodes of a graph. Outside the description of a network size by the number of nodes and edges, and its total length and traffic, several measures are used to define the structural attributes of a graph the diameter, the number of cycles, and the order of a node.ĭiameter ( d). Comparing the evolution of a transport network at different points in time.Comparing different transportation networks at a specific point in time.Expressing the relationship between values and the network structures they represent.Several measures and indices can be used to analyze network efficiency, with many initially developed by Kansky in the 1960s: For instance, it may not be at first glance evident to assess which of two transportation networks is the most accessible or the most efficient. Transportation networks are composed of many nodes and links, and as they rise in complexity, their comparison becomes challenging. Graph theory relies on several measures and indices that assess the efficiency of transportation networks. ![]()
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