Structural аnalysis of the Ethereum smart contract interaction network

Abstract

The rapid development of decentralized finance has led to the emergence of protocols in which dozens of smart contracts interact through chains of public function calls, token transfers, and price oracle calls. As a result, both security auditing and execution cost optimization increasingly depend on understanding the structure of these interactions, rather than the properties of a single contract considered in isolation. The aim of the work is to develop and study a graph model of the Ethereum smart contract interaction network based on the adjacency matrix and determine its structural characteristics to form a structural portrait of the network. The paper applies graph-theoretic methods to study the structure of the smart contract network modeled on the MakerDAO protocol. The network is represented by two adjacency matrices: a directed matrix A, which reflects the actual structure of calls between contracts, and a derived undirected matrix B, intended for classical topological and spectral analysis. A compact set of structural metrics is computed for each representation, The set includes four groups: basic topological metrics (density, input and output degrees), connectivity and distance metrics (average shortest path length, diameter, clustering coefficient), centrality metrics (betweenness centrality, closeness centrality, and Katz centrality ), and spectral metrics (spectral radius of the matrix A and Fiedler value of the undirected Laplacian). The results demonstrate a sparse, structurally shallow network, the directed representation of which is completely acyclic. A small group of structurally dominant contracts is also revealed – primarily the central accounting contract and the intermediary contract-management interface, which combine high values of betweenness centrality and Katz centrality in both representations. The results obtained characterize the main structural properties of the network and identify the contracts through which most of the interaction paths pass, forming the structural basis for the next stage of research - cooperative game-theoretic optimization of smart contract execution routes in Ethereum ecosystems. The result of the work is the construction of a model, which was called the structural portrait of the smart contract interaction network and makes it possible to identify its features.