The Starfish Topology (RADIO Token's Primary Utility)

Another major problem in today's DEX's that RadioShack is planning to solve is the issue of liquidity dispersion. The following graph shows the typical liquidity dispersion model currently in use throughout the industry:
Typical DEX topology
Solid lines denote deep liquidity pools, thinner lines denote medium size liquidity pools, and dotted lines show very shallow liquidity pools. Since liquidity pairs are often added without much planning, the graph's connectivity is low and most paths involve thinly spread liquidity pairs. In graph theoretic terms:
The average distance of the graph (adjusted for depth of liquidity) is high and connectivity is low
The diameter of the graph is large
For example, in the above graph, to swap from USDT to DAI two possible paths are available:
Route #1 - Direct from USDT to DAI: That's the dotted edge connecting the two nodes (USDT and DAI): This edge has low liquidity therefore the price impact and slippage will be high. This is not an ideal path.
Route #2 - USDT > USDC > WETH > DAI: This path avoids very low liquidity edges. But involves 3 hops of varying degrees of liquidity. It's better than Route #1 but still not ideal.
The above example shows the main issue with chaotic and dispersed liquidity addition. To solve this problem, RadioShack needs to significantly reduce the diameter of the graph, and increase its liquidity-adjusted connectivity. This will be achieved by using a single large-degree node (the RADIO node) to create what we refer to as The Starfish Topology. In this topology, the tokens are mostly linked with the RADIO token in a hub and spokes structure, which has a much lower liquidity-adjusted average distance and a smaller diameter. Furthermore, the Starfish Topology has the benefit of having way fewer edges compared to the previous graph, thus concentrating the liquidity and creating deeper pools that can offer lower price impact and slippage. Furthermore, the Starfish Topology attempts to balance the depth of the liquidity among its 'limbs' by moving liquidity incentives to the thinner but high traffic limbs.
The Starfish Topology
The RADIO token node serves as the central, large-degree node in the Starfish Topology. This is the first and the most important utility of the RADIO token. 
In the new topology, the same USDT to DAI swap in the first chart will go through two efficient and highly liquid paths: USDT > RADIO > DAI 
Important: In the Starfish Topology, as more new tokens are added, the Starfish grows more limbs, and therefore the demand for the RADIO token increases accordingly. The RADIO tokens are locked in more and more pools to provide an efficient swap path for all tokens in the ecosystem.

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