Edge computing (EC) aims to place partial processing resources at the edge datacenters (EDCs) for terminal devices to improve the delivery of content and applications to end users. Compared with traditional centralized cloud datacenters (CDC), the EDCs are distributed on the edge of the network that closer to terminal devices in geographical location for reducing the delay of data transmission between cloud and terminals, and enhancing the quality of services for the time sensitive applications. Currently, the edge datacenter networks (EDCNs) use the tree-hierarchical architecture which inherits the problems of limited bandwidth capacity and lower server utilization. This requires a new design of scalable and inexpensive EDCN infrastructure which enables high-speed interconnection for exponentially increasing number of terminal devices and provides fault-tolerant and high network capacity. In this paper, we propose a novel architecture call Sierpinski Triangle Based (STB) for EDCN which uses Sierpinski fractal to mitigate throughput bottleneck in aggregate layers as accumulated in tree hierarchical architecture. The results of the experiment show that the STB architecture has higher throughput than both traditional tree-hierarchical and DCell architectures from the scale of 12 to 363 servers without link failure happens.