Communication Topology and Information Cascading in Planet 100: Bottleneck Detection and Bandwidth Optimization in 100+ Agent Clusters

Abstract

Communication topology is the substrate upon which all multi-agent coordination operates. In Planet 100's 111-agent cluster, the communication network processes an average of 14,700 inter-agent messages per simulation cycle, carrying decision proposals, evidence bundles, audit queries, and coordination signals across 10 functional zones. The structure of this communication network — which agents talk to which, how much bandwidth each channel carries, and where information bottlenecks form — fundamentally determines the system's governance throughput, decision latency, and failure resilience.

This paper presents a spectral analysis of Planet 100's communication adjacency matrix A in R^{111x111}. We compute the full eigenvalue spectrum of the normalized Laplacian L_norm = I - D^{-1/2} A D^{-1/2} and extract three key insights: (1) the algebraic connectivity lambda_2 = 0.037 indicates a well-connected network with a single bottleneck partition, identified by the sign structure of the Fiedler eigenvector; (2) the spectral gap ratio lambda_2 / lambda_max = 0.018 reveals that the network is far from a random graph (where lambda_2 / lambda_max approaches 1), indicating highly structured communication patterns; and (3) the top 5 eigenvalues account for 73% of the spectral energy, meaning the 111-agent network can be approximated by a 5-community structure without significant information loss.

Based on these spectral insights, we derive an optimal bandwidth allocation algorithm that redistributes communication capacity across edges to minimize the maximum edge utilization (a minimax problem). The algorithm reduces the peak edge utilization from 94.3% to 61.7%, eliminating the cascading failure risk that occurs when a single overloaded edge drops messages. We further develop a spectral routing protocol that routes messages through the network according to the eigenvector decomposition of the Laplacian, achieving 91.4% of the theoretical maximum throughput — a 2.3x improvement over the baseline shortest-path routing.

1. Introduction

In a 111-agent governance system, the number of possible directed communication channels is 111 * 110 = 12,210. The actual Planet 100 network uses 847 active edges (6.9% density), reflecting the sparse but structured nature of governance communication. Not all agents need to communicate with all others; rather, communication patterns follow the governance hierarchy, with dense intra-zone communication and sparse inter-zone links mediated by designated gateway agents.

The challenge is that this sparse structure creates vulnerability. When a gateway agent becomes overloaded or fails, entire zones can become disconnected from the governance network, stalling decision pipelines and creating information black holes where critical signals are lost. Traditional network engineering approaches — load balancing, redundant links, circuit breakers — provide partial solutions but lack the theoretical foundation to guarantee optimal performance in governance-constrained networks.

Spectral graph theory provides the mathematical tools needed to analyze communication networks at scale. The eigenvalues and eigenvectors of the graph Laplacian encode global structural properties of the network: connectivity, clustering, bottleneck locations, and optimal partitions. By applying these tools to Planet 100's communication graph, we can identify structural vulnerabilities before they manifest as governance failures, design optimal routing strategies that respect governance constraints, and allocate bandwidth to maximize throughput while preserving audit trail integrity.

2. Communication Network Construction

2.1 Adjacency Matrix Definition

We construct the weighted adjacency matrix A in R^{111x111} from 10,000 simulation cycles of Planet 100 operation. The entry A_{ij} represents the time-averaged message rate (messages per cycle) from agent a_i to agent a_j. We apply a noise threshold of 0.1 messages/cycle, setting A_{ij} = 0 for entries below this threshold to eliminate spurious connections from occasional coordination messages. The resulting matrix has 847 non-zero entries with the following statistics:

2.2 Normalized Laplacian

The normalized Laplacian L_norm = I - D^{-1/2} A D^{-1/2} is preferred over the unnormalized Laplacian L = D - A because it accounts for heterogeneous degree distributions. The normalization ensures that eigenvalue magnitudes reflect the relative importance of graph cuts rather than absolute edge counts, which is critical for a network where agent degrees span a 4x range (from 5 to 31).

We symmetrize the directed adjacency matrix using A_sym = (A + A^T) / 2 before computing the Laplacian, as spectral theory for directed graphs requires more complex treatment involving singular values of the transition matrix. The symmetrization loses directionality information, which we recover in the routing analysis (Section 5) by working directly with the asymmetric transition probability matrix P = D^{-1} A.

3. Spectral Analysis of the Communication Graph

3.1 Eigenvalue Spectrum

The eigenvalue spectrum of L_norm reveals the multi-scale structure of the communication network. The first several eigenvalues are:

lambda_1 = 0 (trivial), lambda_2 = 0.037, lambda_3 = 0.089, lambda_4 = 0.142, lambda_5 = 0.198, lambda_6 = 0.371, ..., lambda_111 = 1.97

The key structural indicators are:

• Algebraic connectivity (lambda_2 = 0.037): This small but non-zero value confirms that the network is connected (no isolated components) but has a weak point — a cut that, if severed, would nearly partition the network. The Fiedler vector (eigenvector corresponding to lambda_2) identifies this cut.
• Spectral gap (lambda_3 - lambda_2 = 0.052): The gap between the second and third eigenvalues is relatively large compared to lambda_2, indicating that the primary bottleneck partition is well-separated from secondary structural features.
• Eigenvalue clustering: The first 5 eigenvalues are clustered below 0.2, followed by a jump to lambda_6 = 0.371. This 5-community structure aligns with the governance hierarchy: the 10 zones naturally cluster into 5 functional groups based on communication affinity.

3.2 Fiedler Vector and Bottleneck Identification

The Fiedler vector v_2 (eigenvector of lambda_2) assigns a real value to each of the 111 agents. The sign of v_2(a_j) determines which side of the minimum bisection agent a_j belongs to. Agents with v_2(a_j) close to zero lie near the bottleneck — they are the bridge nodes connecting the two halves of the near-partition.

In Planet 100, the Fiedler vector identifies 7 agents with |v_2| < 0.01:

These 7 agents carry 41.3% of all cross-partition communication despite representing only 6.3% of the population. A failure of any single bridge agent increases cross-partition latency by an average of 340%, and simultaneous failure of any 3 bridge agents causes a full network partition with probability 0.89.

3.3 Community Detection via Spectral Clustering

Using the first 5 eigenvectors of L_norm as feature vectors and applying k-means clustering with k = 5, we identify the following community structure:

• Community C1 (Operational Core, 37 agents): Operators (Z2), Analysts (Z3), and half the Sentinels (Z6). Primary function: task execution and monitoring.
• Community C2 (Strategic Command, 19 agents): Strategists (Z1), Synthesizers (Z8), and Diplomats (Z5). Primary function: planning and cross-zone coordination.
• Community C3 (Compliance Layer, 22 agents): Auditors (Z4), Archivists (Z7), Observers (Z10). Primary function: governance verification and knowledge management.
• Community C4 (Execution Frontier, 18 agents): Executors (Z9), remaining Operators, and a subset of Sentinels. Primary function: final-stage action execution with HITL gates.
• Community C5 (Adaptive Bridge, 15 agents): Mixed-role agents that dynamically shift between communities based on workload. These agents have high betweenness centrality and serve as adaptive bridges.

The modularity score of this 5-community partition is Q = 0.47, indicating moderate but significant community structure. The inter-community edges constitute only 12.3% of total edges but carry 38.7% of total message volume, confirming that cross-community communication is sparse but high-bandwidth.

4. Information Cascading and Failure Propagation

4.1 Cascade Model

We model information cascading as a threshold contagion process on the communication graph. When an agent a_j fails to process a message within its deadline, it generates a backpressure signal that propagates to all upstream agents. If the backpressure exceeds a threshold theta at any upstream agent, that agent also begins dropping messages, triggering a cascade. The cascade dynamics are governed by:

sigma_j(t+1) = H(sum_{i in N(j)} A_{ij} * sigma_i(t) - theta_j)

where sigma_j in {0, 1} is the failure state of agent a_j, H is the Heaviside step function, and theta_j is the failure threshold. The cascade size S (number of agents that enter failure state) depends on the initial failure location and the network topology.

4.2 Cascade Risk Assessment

We simulate single-agent failures at each of the 111 positions and measure the expected cascade size E[S]. The results reveal a strongly heterogeneous risk landscape:

• Low-risk failures (E[S] < 3): 78 agents (70.3%). Failures at these peripheral agents affect at most their immediate neighbors and are contained by local buffering.
• Medium-risk failures (3 <= E[S] < 15): 26 agents (23.4%). These agents occupy intermediate positions and their failure can propagate through a single community.
• High-risk failures (E[S] >= 15): 7 agents (6.3%). These are precisely the Fiedler bridge agents identified in Section 3.2. Their failure triggers cross-community cascades affecting 15-47 agents.

The expected cascade size correlates strongly with the inverse of the Fiedler vector magnitude: E[S] ~ |v_2(a_j)|^{-1.4}, with R^2 = 0.87. This confirms that spectral analysis of the communication graph provides a reliable predictor of cascade risk without requiring expensive Monte Carlo simulation.

5. Bandwidth Allocation and Routing Optimization

5.1 Problem Formulation

The bandwidth allocation problem seeks to distribute a total communication budget B_total across the 847 active edges to minimize the probability of cascade failures. We formulate this as a minimax optimization:

minimize max_{(i,j) in E} f_{ij} / c_{ij}

subject to sum_{(i,j) in E} c_{ij} = B_total, c_{ij} >= c_min for all edges, and flow conservation at each node. Here f_{ij} is the expected message flow on edge (i,j), c_{ij} is the allocated capacity, and c_min is the minimum viable capacity for governance messages.

5.2 Spectral Bandwidth Allocation

We solve the minimax problem using a spectral decomposition approach. The key insight is that the optimal bandwidth allocation is proportional to the expected flow, which can be estimated from the stationary distribution of the random walk on the communication graph. The stationary distribution pi satisfies pi = pi * P, where P = D^{-1} A is the transition matrix. The expected flow on edge (i,j) is then:

f_{ij} = pi_i P_{ij} (total message rate)

The optimal capacity allocation is c_{ij} = B_total f_{ij} / sum_{(k,l)} f_{kl}, subject to the minimum capacity constraint. This closed-form solution avoids iterative optimization and can be computed in O(|V|^2) time using power iteration for the stationary distribution.

5.3 Spectral Routing Protocol

Beyond static bandwidth allocation, we develop a dynamic routing protocol that uses the eigenvector decomposition of the Laplacian to route messages. For a message from agent a_s to agent a_t, the spectral route is computed as:

path(s, t) = argmin_{P in paths(s,t)} sum_{(i,j) in P} (f_{ij} / c_{ij}) + mu * |P|

where the first term minimizes congestion along the path and the second term (weighted by mu) penalizes path length to bound latency. The spectral embedding of the network (positions in the eigenvector space) provides efficient approximate solutions: the spectral distance d_spec(s, t) = || v(s) - v(t) ||_2 (where v(s) is the vector of eigenvector components for agent s) correlates with the optimal path cost (R^2 = 0.79), enabling O(1) routing decisions with only logarithmic-factor suboptimality.

5.4 Results

The spectral bandwidth allocation and routing protocol yield the following improvements over the baseline (uniform allocation with shortest-path routing):

The throughput improvement of 2.3x comes primarily from eliminating the bottleneck edges that were operating near capacity and dropping messages. By redistributing load according to the spectral flow analysis, the network achieves nearly uniform utilization across all edges, converting wasted capacity on underutilized edges into productive throughput.

6. Real-Time Eigenvalue Monitoring for Bottleneck Detection

6.1 Dynamic Spectral Monitoring

The eigenvalue spectrum of the communication graph is not static — it evolves as agents join, leave, or change their communication patterns. We develop a real-time monitoring system that tracks lambda_2 (algebraic connectivity) and the Fiedler vector at each simulation cycle. A sudden drop in lambda_2 indicates the formation of a new bottleneck or the weakening of an existing bridge. We define the Spectral Health Index (SHI) as:

SHI(t) = lambda_2(t) / lambda_2_baseline * (1 - max_j |delta v_2(j, t)|)

where lambda_2_baseline is the steady-state algebraic connectivity and delta v_2(j, t) is the change in the Fiedler vector component for agent a_j between consecutive cycles. SHI = 1 indicates a healthy network with stable bottleneck structure; SHI < 0.5 triggers an alert for potential cascade risk.

6.2 Predictive Bottleneck Alerts

By tracking the temporal derivative d(lambda_2)/dt, we can predict bottleneck formation 15-30 cycles before the bottleneck becomes critical. The prediction model uses exponential smoothing:

lambda_2_predicted(t + delta) = lambda_2(t) + (d(lambda_2)/dt)_smoothed * delta

When lambda_2_predicted drops below the critical threshold lambda_crit = 0.015 (determined empirically as the point where cascade probability exceeds 20%), the system preemptively activates redundant bridge agents from Community C5 (the adaptive bridge community). This predictive approach reduces cascade incidents by an additional 47% compared to reactive monitoring.

7. Integration with MARIA OS Governance Framework

The spectral analysis framework integrates with the MARIA OS governance architecture at three levels. First, the community structure identified by spectral clustering maps directly to the MARIA coordinate zones, validating the governance hierarchy design. Second, the Fiedler bridge agents are automatically assigned elevated governance privileges — their actions are audited at higher frequency and their fail-closed gates have tighter thresholds, reflecting their disproportionate impact on network health. Third, the spectral routing protocol respects governance boundaries: messages that cross zone boundaries are automatically tagged with governance metadata (source coordinate, destination coordinate, decision pipeline stage) to maintain audit trail continuity.

The bandwidth allocation algorithm is constrained to allocate at least 15% of each edge's capacity to governance traffic (audit queries, evidence bundles, gate evaluations), ensuring that high data throughput cannot starve governance communication. This constraint is encoded as a lower bound in the minimax optimization and has negligible impact on total throughput (< 2% reduction) because governance traffic is inherently low-bandwidth but high-priority.

8. Conclusion

The communication topology of Planet 100's 111-agent cluster is not merely an implementation detail but a first-class architectural concern that determines governance effectiveness. Spectral analysis of the adjacency matrix reveals the network's hidden structure: 5 functional communities connected by 7 critical bridge agents, with a characteristic spectral gap that distinguishes it from both random graphs and idealized hierarchies.

The practical contributions of this work are threefold. First, eigenvalue-based bottleneck detection provides a computationally efficient alternative to Monte Carlo simulation, enabling real-time monitoring of network health. Second, spectral bandwidth allocation achieves 2.3x throughput improvement by redistributing capacity from underutilized edges to critical paths, simultaneously reducing cascade probability by 84%. Third, the spectral routing protocol achieves 91.4% of theoretical maximum throughput with only modest latency overhead, demonstrating that spectral methods are practical for real-time agent communication optimization.

As MARIA OS scales to larger agent populations, the spectral analysis framework scales with it. The eigenvalue computation via Lanczos iteration is O(|E| * k) where k is the number of desired eigenvalues, making it feasible for networks with thousands of agents. The Fiedler vector-based bottleneck detection requires only a single eigenvector computation, and the spectral routing protocol makes O(1) per-message decisions after an O(|V|^2) precomputation. These favorable scaling properties position spectral topology analysis as the foundation for communication management in the next generation of MARIA OS deployments.