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Improving the Robustness of the XRP Ledger Network via Edge Augmentation Strategies

Afonso Vilalonga, Orkun İrsoy, João S. Resende, Henrique Domingos, Osman Yağan

arXiv:2608.26380v1cs.CR

TL;DR

The XRP Ledger’s high agreement threshold and connectivity requirements leave consensus vulnerable to targeted disruption. The paper evaluates edge augmentation and rewiring under full and partial participation, finding that augmentation—especially random K-out—improves robustness while preserving more topological similarity.

  • Problem

    The XRP Ledger requires connected trusted validators and 80% agreement, so targeted disruption of connectivity-backbone nodes can threaten consensus.

  • Method

    The paper compares three edge-augmentation constructions with prior rewiring on real XRP Ledger data under full-network and subset participation.

  • Results

    Augmentation generally improves network and quorum robustness over the default topology, with K-out outperforming rewiring and two random connections per node raising quorum values from 11% to 38% and 12% to 33% in one subset setting.

  • Takeaways & Limitations

    Random K-out augmentation offers an effective robustness improvement while maintaining higher Jaccard similarity to the original topology than rewiring.

Abstract

from arXiv · show

The XRP Ledger allows its network participants to select a set of trusted peers within the network (i.e., the Unique Node List (UNL)) and communicate with them to reach consensus on which transactions should be included in the next ledger state. However, its consensus protocol requires significant overlap among participants' UNLs, along with a high agreement threshold among the nodes within each UNL (e.g., 80\%). Consequently, an attacker could disrupt the consensus process in such a network by targeting the nodes that form the network's connectivity backbone and reducing the number of trusted participants that can communicate with one another below the required threshold. In this paper, we evaluate strategies to improve the robustness of the XRP Ledger's existing topology, as measured by our formal definitions of quorum and network robustness, and compare them to a second strategy from prior work. The strategy we present is an addition/augmentation approach, in which new edges are added based on different constructions. The second strategy is a rewiring or edge-replacement approach, in which the overall number of edges is preserved but they are rearranged. For each strategy, we consider two different cases: one in which all nodes participate in the edge construction or rewiring process, and another in which only a subset of nodes participates. Our findings demonstrate substantial improvements in robustness when augmentation strategies are used over the default XRP Ledger topology and show that some augmentation strategies achieve robustness metrics equal to or exceeding the rewiring strategy, even when the number of edges added is small (e.g., three edges per node). Additionally, we show that the random K-out-based augmentation strategy maintains higher topological similarity to the original network than rewiring, as measured by Jaccard similarity.

NOVA LINCS

The XRP Ledger uses trusted validator lists and an 80% agreement threshold, creating vulnerability when targeted attacks disconnect backbone nodes. This paper evaluates augmentation and rewiring strategies to improve network and quorum robustness.

  • The XRP Ledger uses Unique Node Lists (UNLs) of trusted validators to reach consensus on ledger updates.Nodes repeatedly adjust proposals toward the majority view of trusted validators when agreement is insufficient.
  • 80% validator agreement and recommended 90% UNL overlap make connectivity essential for avoiding disrupted consensus.Disconnecting validators can reduce connected agreement below the protocol threshold and enable network partitioning.
  • The paper compares augmentation and rewiring across full-network and subset-participation settings using network and quorum robustness.Its augmentation approach adds edges generated by graph-construction strategies, while prior work rearranges existing edges.
  • Augmentation strategies generally improve both robustness metrics over the default topology, with K-out augmentation outperforming rewiring.The comparison includes realistic constraints such as limited node participation and low K values.
  • Random K-out augmentation preserves more similarity to the original topology than rewiring, measured with Jaccard similarity.The paper also releases an open-source simulation framework.

II. METHODOLOGY

The methodology evaluates how augmentation and rewiring strategies affect XRP Ledger network and quorum robustness.

  • The evaluation measures XRP Ledger network robustness under augmentation strategies.
  • The evaluation measures XRP Ledger quorum robustness under rewiring strategies.
  • The methodology compares both strategy families within a common robustness-evaluation framework.

A. Dataset

The study uses a representative XRP Ledger snapshot derived from two months of hourly network observations and focuses on targeted attacks.

  • 1,290 hourly XRP Ledger snapshots were collected over two months in 2022 for dataset characterization.The study computed node and edge counts, degree statistics, density, and average clustering coefficient.
  • 952 nodes and 15,070 edges characterize the simulation snapshot selected as closest to average network statistics.The snapshot has average degree 31.7, minimum degree 1, maximum degree 342, and a largest connected component of 952.
  • Targeted attacks select nodes by degree or betweenness centrality because random failures were already highly robust.Degree counts connections, while betweenness measures how often a node lies on shortest paths between node pairs.

C. Mitigation Strategies

The paper compares three edge-augmentation constructions with prior rewiring under full and subset participation, emphasizing random K-out as the primary strategy.

  • Augmentation strategies: Three augmentation strategies add edges using random K-out, random edge addition, or preferential K-out constructions.The comparison situates K-out augmentation among alternative graph-construction approaches.
  • Augmentation strategies: Random edge addition adds K · n undirected edges uniformly among non-existing edges, with K ranging from 0 to 10.It serves as an Erdős–Rényi-inspired baseline.
  • Augmentation strategies: Preferential K-out connects each selected node to K peers with probability proportional to current degree.Higher-degree nodes are therefore more likely to receive new connections, following preferential attachment.
  • Augmentation strategies: Random K-out gives every participating node exactly K uniformly random new peers, producing a more uniform added degree distribution.Prior work motivates it because K ≥2 achieves high-probability connectivity with O(n) edges, versus O(n log n) for Erdős–Rényi graphs.
  • Rewiring and participation: Rewiring preserves the edge count while adjusting low-degree to high-degree neighbor ratios toward 1:1 across 1 to 25 iterations.Both augmentation and rewiring are also tested on subsets containing 20% to 100% of nodes.

D. Attack Simulations and Measuring Robustness

The study measures network and quorum robustness through repeated targeted-attack simulations, using critical attack sizes to quantify when connectivity or consensus fails.

  • Simulation procedure: 300 independent repetitions estimate average critical attack sizes for each augmentation K and subset-size configuration, with rewiring evaluated across subset sizes.Each repetition uses a unique random seed, while selected nodes, target connections, and validator sets vary between repetitions.
  • Validator assignment: Validator sets contain 34 randomly selected nodes, with degree-proportional and inverse-degree policies used to assess sensitivity to validator assignment.The 34-node set matches the recommended UNL size when the dataset was collected.
  • Sensitivity analysis: The main conclusions remain consistent across random, degree-proportional, and inverse-degree validator assignment methods.Full results for the alternative assignment policies are provided in Appendix A.
  • Attack procedure: Targeted attacks remove node fractions sequentially from 0% to 100% in 2% increments, restoring the network after each metric reaches its failure threshold.The resulting graph is denoted ˜G(p), where p is the fraction of removed nodes.
  • Robustness metrics: Network robustness uses p*_network, the fraction of removed nodes required to fragment the network below half its original size.The metric is based on the relative size of the largest connected component after node removals.
  • Robustness metrics: Quorum robustness uses p*_quorum, the fraction of removed nodes required to halt consensus when the largest connected validator component falls below threshold Q.For XRP Ledger consensus, Q = 0.80, corresponding to at least 28 connected validators in a 34-validator UNL.

III. ROBUSTNESS ANALYSIS

The paper next presents the results of its robustness analysis.

  • The paper presents the results of its robustness analysis.

A. Comparison of Augmentation Strategies

At full participation, random K-out augmentation outperforms random edge addition and preferential K-out across all four targeted-attack robustness scenarios.

  • Random K-out augmentation outperforms random edge addition and preferential K-out across all four robustness scenarios at full participation.The comparison covers both network and quorum robustness under both attack types.
  • Random edge addition improves the default topology but is slightly less robust than K-out augmentation for the same K, particularly for quorum robustness.
  • Preferential K-out performs noticeably worse, especially at small K, with quorum-robustness gains lagging considerably even at K = 10.Its preferential attachment concentrates new edges on already high-degree nodes targeted in the attack scenarios.
  • Random K-out distributes new edges uniformly across participating nodes and therefore consistently achieves the best robustness among the three strategies.Because it is the strongest augmentation strategy, the remaining analysis compares it with rewiring across subset sizes.

B. K-out Augmentation Strategy Applied to Subsets

K-out augmentation substantially improves network and quorum robustness under targeted attacks, including when only a subset of nodes receives new connections. The effect depends on both subset size and K.

  • Robustness improvements: Small K values, including K up to 4, produce significant improvements in both network and quorum robustness for feasible subset sizes such as 40% and 60%.These results indicate that augmentation remains effective without involving the entire network.
  • Robustness improvements: 11% to 38%: quorum robustness under high-degree attacks with K = 2 and a 60% participating subset.Under high-betweenness attacks, quorum robustness also rises from 12% to 33% in the same setting.
  • Dependence on subset size and K: Increasing subset size makes differences between K values more pronounced, while smaller subsets reach performance plateaus at lower K values.The 80% and 100% subsets show substantial differences between K values and higher plateau thresholds.

C. Comparison Between the K-out Augmentation and Rewiring Strategies

The K-out augmentation strategy can match or exceed rewiring with relatively small K values while preserving more of the original topology. It also requires less coordination because nodes independently add connections rather than repeatedly replacing edges.

  • Evaluation setup: Rewiring performance is evaluated across subset sizes using robustness curves whose axes, rows, and columns encode iterations, critical attack size, robustness metric, and attack type.Table I compares the smallest K values at which augmentation reaches or exceeds rewiring for matching subsets.
  • Robustness comparison: For high-degree attacks, augmentation generally matches or exceeds rewiring, with K ≥4 producing nearly identical p∗ values in an exceptional 80% network-robustness case.The difference in that case appears only after the second decimal place.
  • Topology preservation: At 80%-100% subsets, K = 3 augmentation matches rewiring gains at around 20-25 iterations while retaining Jaccard similarity around 0.85 versus well below 0.5 for rewiring.Augmentation therefore keeps nearly three times more of the original topology intact in this comparison.
  • Deployment trade-offs: Rewiring preserves the total edge count but removes and replaces connections, whereas K-out augmentation independently adds K random connections per node without the same coordination requirements.Rewiring requires iterative neighbor-degree inspection, coordination, and information sharing.

IV. CONCLUSION

The paper evaluates graph-construction augmentations for improving XRP Ledger network and quorum robustness, comparing them with prior rewiring work under full and partial participation. K-out augmentation generally improves both metrics and outperforms rewiring, while also suggesting broader decentralized-network applications.

  • Conclusion: The study applies graph constructions to the XRP Ledger and formally evaluates their effects on network and quorum robustness.It compares augmentation strategies with prior rewiring under full and subset participation.
  • Conclusion: Augmentation strategies generally improve both robustness metrics over the default network, with K-out augmentation outperforming rewiring.The conclusion also identifies potential applications to other decentralized networks as a direction for future study.

APPENDIX A SENSITIVITY TO VALIDATOR-SELECTION POLICY

The appendix tests whether the paper’s conclusions depend on how validators are selected. Across degree-proportional and inverse-degree policies, K-out augmentation retains its robustness advantage relative to rewiring, while degree-proportional selection leaves less room for improvement.

  • Experimental setup: Validators are assigned synthetically because the XRP Ledger dataset does not identify which nodes serve as validators.The main experiments select validators uniformly at random from all nodes; the appendix evaluates alternative policies.
  • Degree-proportional selection: Degree-proportional selection makes the baseline network more robust because high-degree nodes are more likely to be protected as validators.Consequently, augmentation and rewiring have smaller incremental gains under this policy.
  • Inverse-degree selection: Inverse-degree selection makes the baseline network more vulnerable, but the overall comparison between augmentation and rewiring remains consistent.This policy favors low-degree nodes rather than central hubs.
  • Inverse-degree selection: Random K-out augmentation matches rewiring at relatively small K values and continues improving robustness as K increases under inverse-degree selection.The result supports the persistence of K-out augmentation’s advantage across validator-selection assumptions.
  • Overall conclusion: K-out augmentation achieves the same robustness level as rewiring while preserving more of the original network topology across validator-selection assumptions.This is the appendix’s overall conclusion about sensitivity to validator-selection policy.
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