The EU Rapid Alert System for Food and Feed (RASFF) is the core cross-border risk-communication backbone of the EU food-safety regime. It operates within the Alert and Cooperation Network (ACN) alongside the Administrative Assistance and Cooperation mechanism (AAC) and other specialized modules under Regulation (EU) 2017/625 (Official Controls Regulation) (European Commission, n.d.b; Regulation (EU) 2017/625 of the European Parliament and of the Council of 15 March 2017 on official controls and other official activities performed to ensure the application of food and feed law, rules on animal health and welfare, plant health and plant protection products, amending Regulations (EC) No 999/2001, (EC) No 396/2005, (EC) No 1069/2009, (EC) No 1107/2009, (EU) No 1151/2012, (EU) No 652/2014, (EU) 2016/429 and (EU) 2016/2031 of the European Parliament and of the Council, Council Reg, n.d.). RASFF disseminates notifications on food, feed, and food-contact materials (FCMs) to support rapid, coordinated control actions across member states and partners. This institutional remit and modular ACN architecture motivate longitudinal, multi-layer analytics (e.g., by notification type) and cross-entity network modelling (European Commission, n.d.e).

Public interfaces (RASFF Window) and ACN documentation enable reproducible data extraction and typology-consistent segmentation Alert, Border Rejection, Information for Attention, and Information for Follow-up, which is essential for methodological clarity when constructing directed, type-specific graphs and decision matrices (European Commission, n.d.c).

Classical centrality indices quantify complementary structural roles: degree (exposure/participation), betweenness (brokerage along geodesics), closeness (access/reach), and eigenvector (importance by association). Freeman formalized (Freeman, 1977) betweenness and clarified centrality concepts, while Brandes introduced (Brandes, 2001) the near-linear-time algorithm, which is now standard at scale. For directed or not strongly connected layers typical in alert networks, harmonic closeness has strong axiomatic support and a clear interpretation via network efficiency (Boldi and Vigna, 2014), addressing path-incompleteness where standard closeness becomes ill-posed. Beyond definitions, axiomatic and efficiency-based treatments justify preferring harmonic variants on these graphs, improving the interpretability of “peripheral yet risk-critical” actors that are widely reachable but have limited outreach (Latora and Marchiori, 2001). Food systems and public health applications show that network structure concentrates risk along recurrent corridors. Recent RASFF-focused studies (Katikou, 2023) construct origin–distribution graphs to examine long-horizon patterns and bottlenecks; the RASNEX tool illustrates how supply-chain relations can be mined from notifications for incident analysis (Lorenzen et al., 2021). Empirically, structural centrality and risk intensity need not coincide, motivating dual-lens analysis. Network science further shows that influential spreaders often sit in k-core regions rather than at the highest degree or betweenness, explaining observed divergences and supporting multilayer/sensitivity analyses (Kitsak et al., 2010).

Multi-criteria decision making (MCDM) synthesizes heterogeneous indicator counts, severities, centralities, and trade volumes into auditable priority lists (Hwang and Yoon, 1981). The Entropy Weighting Method (EWM) derives objective criterion weights from dispersion (Shannon entropy), thereby avoiding subjective elicitation and enabling cross-scenario sensitivity tests. EWM is frequently coupled with distance or outranking-based rankers in food-risk contexts to balance frequency/severity against structural factors (Zhu et al., 2020; Kumar et al., 2021). Among rankers, TOPSIS (closeness to positive/negative ideals) and VIKOR (compromise programming via S, R, and Q indices) are classical choices with well-studied behavior under normalization and weighting; PROMETHEE II offers an outranking perspective (net flows) that can be simplified to step-function preferences when robust ordering is prioritized over fine-grained trade-offs (Brans et al., 1986; Opricovic and Tzeng, 2004). These methods form reliable baselines for inspection design and regulatory prioritization. Emerging strands fuzzy MCDM (to encode linguistic uncertainty) and DEMATEL (to model causal influence among criteria) complement EWM+TOPSIS/VIKOR/PROMETHEE when expert judgment, causal structure, or uncertainty must be explicit (Hajiaghaei-Keshteli et al., 2023; Hezam et al., 2024; Ulutaş et al., 2024; Esmaeili et al., 2025).

An increasingly used, yet still methodologically limited, line of work integrates network analytics with multi-criteria decision-making (MCDM) to prioritize interventions in food systems and public health. Typical pipelines compute centrality measures from single- or multi-layer networks to capture structural importance, and then fuse these indicators with notification volume and severity variables using entropy-weighted TOPSIS/VIKOR or PROMETHEE. Weight-perturbation sensitivity analyses are often applied to evaluate the stability of the resulting rankings (Sari et al., 2025). RASFF-based network studies consistently reveal uneven risk corridors and recurring origin-notifier dyads. Moreover, product-hazard niches can elevate otherwise peripheral nodes to risk-critical status; this divergence between structural centrality and risk intensity is precisely what hybrid network MCDM frameworks aim to surface and operationalize for targeted inspections and import-control prioritization. Table 1 contrasts representative prior approaches with the present study, which integrates network analysis and MCDM to address limitations related to risk prioritization, structural characterization, and reliance on a single decision model.

The dataset consists of RASFF notifications from 2020 to 2024, covering food, feed, and food-contact materials. It includes the following fields: notification, date, classification (Alert, Border Rejection, Information-Attention, Information-Follow-up), origin, distribution, concern, and auxiliary text (subject/measures) used upstream for de-duplication and taxonomy harmonization. All records are cleaned by replacing missing values with empty strings and normalized to a consistent country and taxonomy vocabulary. The processed data are then used to produce two downstream outputs: (a) decision matrices for multicriteria decision-making (MCDM), represented by summary files such as mcdm1.csv for countries and product_summary.csv for product categories, where each row corresponds to a country or category and columns capture criteria such as centrality indicators in the total graph and volume or severity-weighted alert metrics; and (b) Edge lists were conceptually defined and used within the NetworkX framework to compute centrality measures for each notification type and for the overall (Total) network, although explicit graph visualization was not part of the workflow.

The surveillance pathways are modelled as directed graphs comprising four strata: Total (all notifications), Alert, Border Rejection, Information for Attention, and Information for Follow-up. The nodes represent countries mentioned in the origin, distribution, or concern fields. For each notification, directed edges are established from each origin country to each distribution country (excluding self-links and non-country tokens) and from each distribution country to each concerned country. When the distribution field is empty or excluded during processing, fallback edges are created directly from the origin to the concern.

Edge-weight treatment. Networks are constructed as unweighted, binary directed graphs: an edge indicates the presence of at least one observed origin–distribution or distribution–concern linkage. Multiple notifications producing the same ordered pair are collapsed into a single edge (i.e., no parallel edges), thereby avoiding duplication of signal intensity in the network structure. Notification frequency and severity are captured separately as criteria in the MCDM decision matrices, thereby preventing double-counting.

Self-link handling. Self-loops are excluded by enforcing u≠v for every candidate edge u→v.

Formally, for each notification: (i) for every origin country iand distribution country j, add an edge i→j if i≠j; (ii) for every distribution country j and concerned country k, add an edge j→k if j≠k and (iii) if the distribution field is empty after filtering, add a fallback edge i→k (subject to i≠k). The resulting edges are organized into separate directed graphs corresponding to each notification category: total, alerts, border rejections, information for attention, and information for follow-up. Each edge is assigned to its respective graph based on the notification classification, which is standardized to consistent lowercase labels such as “alert notification” and “border rejection notification” for each notification type.

All centralities are computed on each layer L (and on Total), then min–max scaled to [0, 1] for comparability:

where σ_st is the number of shortest (directed) paths s→t and σ_st(i) those passing through i.

For a node i in a graph with n nodes,

where d(i, j) is the shortest-path distance from i to j.

computed on the largest strongly connected subgraph if necessary.

These centralities (plus simple volumes like alert counts or severity-weighted counts) become the criteria for MCDM.

We prepare two matrices:

All criteria are treated as beneficial (larger⇒higher risk/priority). Any cost-type indicators are inverted upstream.

Column normalization (Min–Max), applied to each column j:

Form column proportions pij=zij/∑izij (with a tiny constant for zeros). Entropy and divergence (Kumar et al., 2021):

Normalize to get weights:

(a) TOPSIS (distance to ideal) (Hwang and Yoon, 1981)

Weighted matrix v_ij = w_jz_ij. Positive/negative ideals:

Euclidean distances and closeness:

Rank by CC_i descending.

(b) VIKOR (compromise) (Opricovic and Tzeng, 2004)

Let fj*=maxizij, fj-= minizij.

Define:

With S*=miniSi,  S-=maxiSi and R^*, R⁻ Analogously, the index

using v = 0.5 and ε≈10⁻⁹. Rank by Q_i ascending.

(c) PROMETHEE II (simplified, as coded) (Brans and Vincke, 1985)

Binary preference per criterion:

Leaving-flow surrogate:

Rank by ϕ(a) descending.

Generate perturbed weights w~ by multiplicative noise and renormalization (Triantaphyllou and Sánchez, 1997):

For each w~, recompute TOPSIS ranks; report the average rank over 100 runs as a stability summary.

Centrality measures summarize how the surveillance network is organized and which countries or product categories play key structural roles. For example, some actors function as hubs with many connections, others act as brokers that link otherwise separate parts of the network, and some occupy positions that allow information to reach them quickly. The multi-criteria decision-making (MCDM) framework then combines these network-based signals with notification volume and severity information to produce risk-priority rankings for both countries and product categories. Comparing rankings from different sources, for instance, an MCDM-based ranking versus a structure-only ranking, helps distinguish actors that are high-risk despite limited network prominence from those that are structurally central but not necessarily risk-intensive. This distinction supports more targeted and defensible choices in inspection planning and other control measures.

To assess robustness beyond descriptive reporting, we evaluate cross-method rank agreement, weight-perturbation sensitivity (σ = 0.1, 100 iterations; renormalized), and temporal consistency via year-wise backtesting over 2020–2024. Agreement is measured using Spearman's ρ and Kendall's τ over rank vectors with two-sided tests (Table 2), indicating strong concordance across methods.

Table 3 summarizes network-level metrics across the five notification layers. The Total and Alert layers are comparatively dense (0.1081 and 0.1100, respectively), whereas the Border Rejection layer is substantially sparser (0.0372), reflecting a narrower set of pathways specific to import-control actions. Average clustering is high in the Total and Alert layers (approximately 0.76), indicating pronounced triadic closure and tightly connected subnetworks, consistent with regional coordination among closely interacting member states.

Across all layers, degree assortativity is negative (from −0.2827 to −0.5575), implying disassortative mixing in which high-degree hubs preferentially connect to lower-degree peripheral nodes. This hub–periphery organization is consistent with surveillance systems where a small set of highly connected countries concentrates reporting and redistribution links. Finally, the network diameter remains small (3–4) across layers, suggesting short paths and efficient reachability, such that notification linkages can traverse the network within a few steps.

The directed origin-to-notifier adjacency heatmap (Figure 1) exhibits a strongly right-tailed distribution of alert flows: a relatively small set of high-intensity dyads (at or above the 90th percentile, annotated) accounts for a disproportionate share of notifications. Restricting the visualization to the top-20 origins and top-20 notifiers highlights persistent corridors linking major import gateways with recurrent exporting partners. Self-flows are removed to emphasize cross-border pathways and to support corridor-level targeting rather than diffuse, uniform surveillance.

Country roles vary markedly across notification types. A compact EU core of Germany, the Netherlands, France, and Belgium remains structurally prominent in most layers, whereas border rejections elevate additional actors (notably Turkey, India, and China) into type-specific, risk-critical positions. Tables 4–8 summarize the centrality profiles underlying these patterns.

Brokerage (betweenness). Betweenness centrality concentrates in a small set of brokers, but the leading broker shifts by layer (Table 4). In the Total and Alerts layers, France and Belgium dominate brokerage (e.g., Total: France 0.0691; Belgium 0.0674; Alerts: France 0.0834). In Border Rejections, brokerage pivots to entry-point interfaces, led by Germany and Spain (Germany 0.1043; Spain 0.1039), with Cyprus, Turkey, and India also salient. Information-for-Attention exhibits especially strong brokerage in Belgium (0.1860), while Information-for-Follow-up returns to a compact broker set headed by France and Belgium.

Reach and accessibility (in-degree, closeness). In the Total and Alerts layers, Belgium and Germany show near-maximal reach and accessibility, reflected in high in-degree and closeness (Total closeness ≈ 0.9314; Alerts ≈ 0.9482; Tables 5, 8). In Border Rejections, closeness peaks at Germany (0.5442) and remains high for Poland, Turkey, the Netherlands, and India, consistent with concentrated inspection touchpoints and port-of-entry interfaces.

Out-degree indicates outward signaling and dissemination (Table 6). In the Total and Alerts layers, outbound ties are strongest for Belgium and France (e.g., Total: Belgium 0.8193; France 0.8149; Alerts: France 0.8605; Belgium 0.8461). In Border Rejections, outbound prominence shifts toward major exporting origins (Turkey 0.2870; India 0.2685; China 0.2500) alongside Germany (0.2500), highlighting recurrent origin-linked rejection pathways.

Embedded influence (eigenvector; k-core). Eigenvector centrality indicates embedded influence within well-connected neighborhoods (Table 7). In the aggregate network, scores are tightly clustered across the core (e.g., Germany 0.1269; Belgium 0.1268; Netherlands 0.1266), reflecting a mutually reinforcing backbone. In Border Rejections, influence steepens and concentrates in the Netherlands (0.2712) and Germany (0.2611), consistent with gateway amplification through second-order connectivity.

To complement shortest-path and eigenvector-based measures, additional centrality diagnostics, including PageRank, HITS hub and authority scores, and k-Core membership was examined. These measures provide convergent evidence regarding the core-periphery organization of the network and clarify whether a country primarily functions as a disseminator of notifications (hub) or as a recipient or endpoint (authority). The results for the top ten countries in the Total network are summarized in Table 9, where consistently high PageRank values, maximal k-Core membership, and balanced hub–authority scores identify a tightly connected core of influential member states.

Zero prevalence varies substantially across criteria, and several measures exhibit notable sparsity (e.g., betweenness shows a high proportion of zeros). Under entropy weighting, such sparsity can increase discriminative power by amplifying differences among non-zero observations. To ensure numerical stability during entropy computation, zero entries are replaced with a small constant ε = 10⁻¹² before logarithmic operations. As shown in Table 10, highly sparse metrics such as betweenness receive larger entropy weights, whereas metrics with negligible sparsity, including eigenvector centrality and PageRank, provide stable baseline contributions. As an external check, alternative weighting schemes produce highly consistent rankings (Entropy vs. CRITIC: ρ = 0.9568; Entropy vs. equal weights: ρ = 0.9714; both p < 0.001), supporting the robustness of the weighting choice.

We integrate structural indicators and risk-intensity criteria using an entropy-weighted MCDM ensemble to obtain regulator-ready priorities. TOPSIS and VIKOR produce a stable top tier Germany (1), the Netherlands (2), France (3), and Belgium (4), followed by Italy, Spain, and Poland (Table 11). PROMETHEE II corroborates this ordering, and sensitivity ranks indicate minimal volatility for the top tier but increasing method/weight dependence in mid- and lower-rank positions (Table 12). Overall, convergence across distance-to-ideal (TOPSIS), compromise programming (VIKOR), and outranking (PROMETHEE II) supports robustness of the leading recommendations, while lower tiers warrant periodic re-estimation to detect rank drift.

At the category level, the ensemble consistently prioritizes Fruits and Vegetables, followed by Nuts/Seeds and Poultry (Table 13). Cereals & Bakery forms the upper-middle tier, while Dietetic foods/supplements and Herbs & Spices remain consistently important, aligning with persistent residue and contamination niches. Food-contact materials and fish occupy the mid-tier, supporting targeted sampling rather than blanket intensification. Taken together, the country- and category-level shortlists suggest pairing corridor-focused controls at core hubs (Germany, the Netherlands, France, Belgium) with intensified sampling in horticulture and poultry, and strengthening documentation and pre-shipment checks for recurrent exporting origins (e.g., Turkey, India, China) in persistently high-ranked categories.

Robustness was assessed via cross-method agreement of the resulting rank orders at both the country and category levels. We quantified concordance using Spearman's ρ and Kendall's τ computed on rank vectors, with two-sided significance testing. At the country level, correlations are near unity, indicating that TOPSIS, VIKOR, and PROMETHEE II yield essentially the same ordering of alternatives (Table 14). Category-level rankings show similarly strong concordance across all method pairs (Table 15). Together, these results indicate that the core conclusions are stable across distinct MCDM paradigms and are unlikely to be artifacts of any single solver.

A consistent finding in the 2020–2024 results is that being structurally central does not always mean being risk-intensive. Centrality measures (e.g., betweenness, closeness, eigenvector, and core membership) indicate which countries sit on major pathways and frequently connect different parts of the network. In contrast, risk intensity captured by notification volume, serious-risk flags, and the category–hazard profile reflects where the burden is concentrated and where incidents tend to be more severe. At the country level, the main EU notifiers (Germany, the Netherlands, France, and Belgium) remain central across layers (Tables 4–8). However, border rejections highlight additional actors, including third-country origins (Turkey, India, and China) and some EU members (e.g., Spain and Poland), that become risk-critical within specific notification types even if they are not among the most central overall. At the category level, the MCDM ensemble consistently ranks Fruits & Vegetables, Nuts/Seeds, and Poultry highest (Table 8), pointing to recurring hazard niches (residues, mycotoxins, and microbiological hazards) that can intensify risk along particular origin → notifier corridors even when those corridors are not structurally dominant.

From a practical perspective, centrality is useful for understanding where signals can spread quickly, but it is not sufficient on its own to decide where inspections should be concentrated. Our hybrid approach addresses this by combining structural indicators (to identify key intermediaries and highly connected hubs) with intensity indicators (to target the highest-burden corridors). This produces a layer-aware allocation that both maintains capacity at core hubs and strengthens controls along risk-intensive routes that may lie outside the aggregate core.

High betweenness countries, France (0.0734), Belgium (0.0685), and the Netherlands (0.0524) act as brokerage nodes (information chokepoints), consistent with evidence that intermediaries can disproportionately influence diffusion processes (Kitsak et al., 2010). The negative degree assortativity coefficient (−0.506) further indicates disassortative mixing, whereby high-degree hubs preferentially connect to lower-degree peripheral countries, yielding hub periphery corridors (Latora and Marchiori, 2001). Figure 2 visualizes the 2020-2024 country-level RASFF network (225 countries, 5,448 connections), with node size proportional to degree centrality and node color encoding betweenness centrality. France attains the maximum betweenness (0.0874), while Belgium exhibits the maximum degree (297). For readability, the plot displays only the top 40 countries by degree.

Our findings support a layer-aware, corridor-focused surveillance strategy. Capacity should remain concentrated at the core hubs. Germany, the Netherlands, France, and Belgium, while pre-border and entry-point controls are intensified for recurrently implicated origins (notably Turkey, India, and China) in fruits & vegetables, nuts/seeds, and poultry. Alerts should trigger rapid risk communication and targeted sampling along high-betweenness dyads; border rejections motivate documentation checks and supplier verification at ports; information for follow-up guides the diffusion of post-incident actions from hubs with high outreach. Composite priorities from the entropy-weighted TOPSIS/VIKOR/PROMETHEE ensemble should be recomputed quarterly, with operational triggers defined on rank changes and brokerage spikes to anticipate shifts in risk corridors.

Results inherit the properties of RASFF notifications, including potential differences in reporting intensity and follow-up practices. Although we adopt closeness and conduct weight perturbation and cross-method checks, centrality and MCDM outputs remain sensitive to edge definitions, normalization choices, and latent under-reporting. Future work should examine multiplex, time-resolved constructions (e.g., hazard-specific layers), integrate trade-flow and supplier-network data, and test fuzzy/causal MCDM (e.g., DEMATEL/ANP) to represent criterion interdependence. Prospective back-testing and pilot deployments with inspectorates can quantify detection yield and refine cost-effective inspection portfolios.