The Transaction Graph

The Dynamic Transaction Graph is a bipartite graph that captures the economic relationships between producers and buyers, with weighted edges representing the cumulative fees from their past transactions. The graph allows the network to dynamically adjust token incentives based on the actual economic activity and pricing power of participants, ensuring a fair and efficient allocation of rewards that adapts to the unique properties of each market, whether location-dependent or location-independent.

Graph Structure#

In Local Protocol, the transaction graph is modeled as a bipartite graph:

$G = (U, V, E)$

• $U$: Set of nodes representing producers (e.g., service providers, sellers).
• $V$: Set of nodes representing buyers (e.g., consumers, users).
• $E$: Set of weighted edges that represent transactions between producers and buyers.

Edge Weights#

The edges $w(u, v)$ in the graph represent the transaction volume between a producer $u$ and a buyer $v$. These weights accumulate over time to reflect the total economic interaction between nodes:

• $w(u, v)$: Weight of the edge, indicating the transaction volume from producer $u$ to buyer $v$.

• $W_u$: Total transaction volume for producer $u$, calculated as:

  $$W_u = \sum_{v \in V} w(u, v)$$

• $W_v$: Total transaction volume for buyer $v$, calculated as:

  $$W_v = \sum_{u \in U} w(u, v)$$

These metrics allow the network to measure a node's total economic contribution, facilitating fair and dynamic token distribution.

Key Features#

1. Dynamic Adjustments#

The transaction graph dynamically adjusts based on participant interactions. As transactions occur, edge weights are updated, causing changes in connectivity and node influence. This creates a self-optimizing system where token distributions reflect the evolving state of the network.

2. Connectivity as a Measure of Value#

The graph not only captures transaction volume but also connectivity:

• Nodes with more connections to well-connected nodes are considered more influential.
• This approach ensures that participants contributing to network growth through broad connectivity earn higher rewards, rather than just high transaction volumes with a single node.

3. Sybil Resistance#

The graph’s structure inherently resists manipulation through Sybil attacks:

• Sybil nodes (fake users) typically form isolated clusters without strong connections to real nodes.
• The graph's weighting system prioritizes connections that enhance network-wide connectivity, making it difficult for isolated Sybil nodes to earn high rewards.

Next Steps#

The transaction graph sets the foundation for the network.