IJCNC 02

ASRA-GNN: ADAPTIVE SIGNED RELATION-AWAREGRAPH NEURAL NETWORK FOR FRIENDRECOMMENDATION

Pharsana Parveen M1
and Stanis Arul Mary A2

Research Scholar, PG and Research Department of Mathematics, Nirmala College for
Women, Coimbatore, Tamil Nadu, India – 641018
2Assitant Professor, PG and Research Department of Mathematics, Nirmala College for
Women, Coimbatore, Tamil Nadu, India – 641018

ABSTRACT

Existing Signed Graph Neural Networks optimize link sign prediction objectives fundamentally misaligned with friend recommendation, while discarding trust asymmetry, edge strength, and adaptive social theory
application. We present ASRA-GNN, addressing these gaps through three contributions: Sign-Aware
Structural Role Attention (SSRA) grounded in four social network theories; a Locally Adaptive Theory
Mixing (LATM) gate replacing TrustSGCN’s binary global threshold with a continuous per-node end-toend learned mixing function; and a Signed Contrastive Recommendation Loss providing the first ranking
objective for signed user-user graphs using observed positive-negative pairs as natural contrastive
anchors. Experiments on Bitcoin-OTC and Bitcoin-Alpha demonstrate an average of Recall@10 of 0.0599,
NDCG@10 of 0.4280, and Precision@10 of 0.0840, outperforming all other baselines.

KEYWORDS

Graph Theory, Signed Directed Graphs, Signed Graph Neural Networks, Friend Recommendation,
Balance Theory, Structural Role Attention.

1. INTRODUCTION

To help users make real connections, social media sites are increasingly using automated friend
recommendations. Friend recommendation operates on a homogenous user-user graph, where
edge weights signify the trust or distrust between the two users. The signed-graph structure is a
perfect semantic signal for this, which does not include any additional information and helps us
to handle user recommendations with a graph-theoretic approach. Signed graph neural networks
(SGNN) have emerged as a recent trend in the primary approach for representations of signed
networks.

The first graph neural network that was explicitly trained on signed networks was SGCN [1]. Its
main addition was the operationalization of balance theory [2] in a GNN propagation model by
relying on a dual-channel architecture: a positive channel, which aggregates messages along
balanced paths and a negative channel, which correlates messages along unbalanced paths. Graph
mining techniques have also been applied to peer-to-peer network analysis for detecting
anomalous structural patterns [3], demonstrating the broader utility of graph-theoretic methods in
network communication systems. SGCN has three significant drawbacks. First, it is undirected in
nature and thus eliminates the asymmetric characteristics of trust relationships. Second, edges are

considered binary signs having no idea of trust strength or intensity. Third, the normalization of
propagation is predetermined and symmetric.

Two advances over SGCN were made by SiGAT [4]. It generalized signed GNN propagation to
directed graphs, retaining the asymmetricity of trust edges and the original attention mechanism
in signed GNNs, based on the Graph Attention Network (GAT) architecture [5]. SiGAT does not
treat all neighbours equally but instead calculates weights of attention using membership in 38
graph motifs following balance theory [2] and status theory [6]. The limitations include
computation of all 38 motifs that are extracted by listing triangles in the graph at a time, which
has a complexity of 𝒪(𝑛^3). Moreover, SiGAT still takes edges as binary signs having no
continuous strength of trust, and its attention mechanism is fully structure-based.

SDGNN [7] provided the solution to the scalability issue of SiGAT by grouping its 38 motifs into
four types of signed directed relations, supporting relation-specific aggregation at linear
precomputation cost. SDGNN also suggested a multi-objective training loss using a combination
of sign prediction, edge direction prediction, and triangle reconstruction [7], which is more
informative than binary cross-entropy. However, SDGNN still has binary edge semantics and no
continuous trust weighting, and the four types of relations are not differentiated by whether they
are unilateral or reciprocal. Its objective in training is fully oriented to link sign prediction
without any ranking element included, and no formal inference pipeline is recommended to be
used LightSGCN [8] used the LightGCN [9] simplification principle of signed networks: nonlinear
propagation layers, weight matrices, and nonlinear activations of propagation layers were
removed, and instead propagation was done by aggregating the neighborhood and combining
layers. This was a simplification, butit is proven to decrease overfitting and enhance
generalization in the signed case. LightSGCN has the major weakness of normalizing the
symmetries of the degrees deterministically, giving weights of aggregation solely based on the
degree of the nodes. LightSGCN assigns the same aggregation weights to two neighbors.
Moreover, LightSGCN is undirected and has binary edges, which is passed to SGCN.

The most recent and the most relevant base is TrustSGCN[10], its key empirical finding was the
inability of the balance theory [2] to generate the correct sign in 18 − 51% of triads in four
benchmark sets. TrustSGCN proposes a trust score for every node based on a separately trained
classifier and also relies on this score to route aggregation either over balance-theory-consistent
routes or other routes over theory-violating nodes. TrustSGCN has four major limitations that are
overcome by ASRA-GNN. First is the trustworthiness score, which is binarized with a globally
fixed threshold of 0.98 that takes a continuous reliability signal and collapses it into a hard binary
decision. Second, the classifier is pre-trained in an unconnected first step and frozen during
training of the GNN so that the pipeline is not end-to-end. Third, computing trustworthiness
demands the construction of ego-networks around all nodes, which is superlinear. Fourth, and
most importantly, TrustSGCNmaximizes a link sign prediction objective and does not
recommend any loss ranking, does not treat explicit distrust as a hard inference constraint, and
does not formalize an inference pipeline.The importance of relationship modeling in mobile
social networkmiddleware further motivates trust-aware graph frameworks foruser-to-user
interaction [11].

We presented ASRA-GNN, a comprehensive end-to-end framework addressing all four identified
shortcomings.Our contributions are threefold, namely, Sign-Aware Structural Role Attention
(SSRA), Locally Adaptive Theory Mixing (LATM), and signedcontrastive recommendation loss.
ASRA-GNN achieves superior or competitive results against all five baselines on Bitcoin-OTC.
ASRA-GNN improves Micro-F1 by 𝟐. 𝟓𝟒% and Macro-F1 by 𝟔. 𝟏𝟖% over the strongest
baseline, TrustSGCN, while achieving a comparable AUC (0.8958 vs 0.91, a difference of <
2.54%).

2. PROBLEM FORMULATION

Let 𝒢 = (𝒱, ℰ, 𝑆, 𝑊) represents asigned directed socialgraph, where 𝒱 = {𝑢1, 𝑢2, … , 𝑢𝑛}
denotes the set of 𝑛 users ℰ ⊆ 𝒱 × 𝒱 is the directed edge set, 𝑆 ∶ ℰ → {+1, −1} is the sign
function, and 𝑊 ∶ ℰ → (0,1] is the edge weight function that encodes the trust strength. For
(𝑢, 𝑣) ∈ ℰ, 𝑠𝑢𝑣 = +1 represents trust and 𝑠𝑢𝑣 = −1 represents distrust. The absence of an edge
(𝑢, 𝑣) denotes an unknown or undiscovered relationship, instead of an explicit distrust.
The positive and negativeneighbor sets of 𝑢 are:
𝑁
+(𝑢) = {𝑣|(𝑢, 𝑣) ∈ ℰ
+}, 𝑁
−(𝑢) = {𝑣|(𝑢, 𝑣) ∈ ℰ
−} (1)
Given 𝒢, the friend recommendation task requires producing, for each query user 𝑢 ∈ 𝒱, a ranked
list 𝑅(𝑢) = {𝑣1, 𝑣2, … , 𝑣𝐾} satisfying 𝑣𝑖 ∉ 𝑁
+(𝑢) (not already a direct friend) and 𝑣𝑖 ∉ 𝑁
−(𝑢)
(not explicitly distrusted). The strict exclusion of 𝑁
−(𝑢) represents the basic inference constraint:
over distrust establishes a structural hard boundary that no embedding score may surpass

3.METHODOLOGY

ASRA-GNN functions based on four consecutive stages: (1) signed directed graph construction
with six-type relation decomposition and structural property precomputation; (2)the Sign-Aware
Structural Role Attention (SSRA) encoder built on LightSGCN-style propagation; (3)the Locally
Adaptive Theory Mixing (LATM) gate; and (4) a multi-objective signed recommendation
training with a two-stage signed inference pipeline.

3.1. Graph Construction

The methodology for the underlying graph construction is detailed as follows, outlining the
transformation of raw data into a structured topological format

3.1.1. Graph Representation in ASRA-GNN

ASRA-GNN represents the social network in form of a signed directed weighted graph:
𝒢 = (𝒱, ℰ, 𝑆, 𝑀) (2)
where 𝒱 = {𝑢1, … , 𝑢𝑛
} is the user set with |𝒱| = 𝑛; ℰ ⊆ 𝒱 × 𝒱 is the directed edge set where
(𝑢, 𝑣) ∈ ℰ denotes that 𝑢 has rated a signed sentiment toward 𝑣; 𝑆: ℰ → {+1, −1} is the sign
function; and 𝑊: ℰ → (0,1] is the continuous weight function. The absence (𝑢, 𝑣) ∉ ℰ denotes an
unknown or undiscovered relationship, conceptually distinct from explicit distrust 𝑠𝑢𝑣 = −1.
The edge set ℰ decomposes into two disjoint signed subgraphs:
ℰ

= {(𝑢, 𝑣) ∈ ℰ|𝑠𝑢𝑣 = +1}, ℰ
− = {(𝑢, 𝑣) ∈ ℰ|𝑠𝑢𝑣 = −1} (3)
with ℰ

∪ ℰ
− = ℰ and ℰ

∩ ℰ
− = ∅. The subgraph 𝒢

= (𝒱, ℰ
+) is the social trust network;
𝒢
− = (𝒱, ℰ
−) is the social conflict network.
All five baselines consist of this decomposition implicitly by maintaining both dual positive and
negative embedding channels, but ASRA-GNN explicit design it as the mathematical foundation
for the six-type relation decomposition and the dual-channel encoder. ASRA-GNN constructs
separate embedding channels ℰ𝑢

and ℰ𝑢
− for each subgraph, emphasizing independent learning
from trust and distrust signals, which is later combined. The graph is directed by design. For any
pair (𝑢, 𝑣), three structurally distinct configurations arise:
(𝑢 →+ 𝑣, 𝑣 ↛ 𝑢), (𝑢 ⇌+ 𝑣), (𝑢 →+ 𝑣, 𝑣 →− 𝑢) (4)

These represent different social meanings −unilateral endorsement, confirmed friendship, and a
conflicted relationship respectively, which cannot be distinguished by an undirected graph. The
signed degree quantities used throughout ASRA-GNN are:
deg𝑜𝑢𝑡

(𝑢) = |𝑁𝑜𝑢𝑡

(𝑢)|, deg𝑖𝑛

(𝑢) = |𝑁𝑖𝑛

(𝑢)| (5)
deg𝑜𝑢𝑡
− (𝑢) = |𝑁𝑜𝑢𝑡
− (𝑢)|, deg𝑖𝑛
− (𝑢) = |𝑁𝑖𝑛
− (𝑢)| (6)
Where the four typed neighborhood sets are:
𝑁𝑜𝑢𝑡

(𝑢) = {𝑣|(𝑢, 𝑣) ∈ ℰ
+}, 𝑁𝑜𝑢𝑡
− (𝑢) = {𝑣|(𝑢, 𝑣) ∈ ℰ
−} (7)
𝑁𝑖𝑛

(𝑢) = {𝑣|(𝑢, 𝑣) ∈ ℰ
+}, 𝑁𝑖𝑛
− (𝑢) = {𝑣|(𝑢, 𝑣) ∈ ℰ
−} (8)
𝑁𝑜𝑢𝑡

(𝑢) is the set 𝑢 actively trusts; 𝑁𝑜𝑢𝑡
− (𝑢) is the set 𝑢 actively distrusts; 𝑁𝑖𝑛

(𝑢) is the set who
endorse 𝑢; 𝑁𝑖𝑛
− (𝑢) is the set who oppose 𝑢. The full signed neighborhood is 𝑁(𝑢) = 𝑁𝑜𝑢𝑡

(𝑢) ∪
𝑁𝑜𝑢𝑡
− (𝑢) ∪ 𝑁𝑖𝑛

(𝑢) ∪ 𝑁𝑖𝑛
− (𝑢), which is the input to SSRA propagation in Section 3.3.
The edge weights 𝑤𝑢𝑣 represent the continuous trust strength, the first novelty among all five
baselines, which considers edges as binary signs. For datasets with explicit ratings (Bitcoin-OTC,
Bitcoin-Alpha), normalization is carried out by:
𝑤𝑢𝑣 =
𝑟𝑎𝑤𝑢𝑣 − 𝑚𝑖𝑛𝑟𝑎𝑤
𝑚𝑎𝑥𝑟𝑎𝑤 − 𝑚𝑖𝑛𝑟𝑎𝑤

𝜀, 𝜀 = 10−6
(9)
For binary-sign datasets such as Slashdot, Epinions, etc weights are initialized from topology and
learned end-to-end (Eq. 11). The weight 𝑤𝑢𝑣 directly scales the message contribution of neighbor
𝑣 in every aggregation layer, so a strongly trusted neighbor (𝑤𝑢𝑣 = 0.9) contributes
proportionally more than a weakly trusted one (𝑤𝑢𝑣 = 0.2).

3.1.2. Signed Directed Relation Decomposition

We proceed by decomposing ℰ into six mutually exclusive and collectively exhaustive relation
types, extending SDGNN’s four SDRs [6] with two reciprocal types motivated by social
exchange theory [10]:
𝑟1: ℰ𝑜𝑢𝑡

= {(𝑢, 𝑣) ∈ ℰ|𝑠𝑢𝑣 = +1, (𝑣, 𝑢) ∉ ℰ}
𝑟2: ℰ𝑜𝑢𝑡
− = {(𝑢, 𝑣) ∈ ℰ|𝑠𝑢𝑣 = −1, (𝑣, 𝑢) ∉ ℰ}
𝑟3: ℰ𝑖𝑛

= {(𝑢, 𝑣) ∈ ℰ|𝑠𝑣𝑢 = +1, (𝑣, 𝑢) ∉ ℰ}
𝑟4: ℰ𝑖𝑛
− = {(𝑢, 𝑣) ∈ ℰ|𝑠𝑣𝑢 = −1, (𝑣, 𝑢) ∉ ℰ}
𝑟5: ℰ𝑟𝑒𝑐

= {(𝑢, 𝑣) ∈ ℰ|𝑠𝑣𝑢 = +1 ∧ 𝑠𝑢𝑣 = +1 }
𝑟6: ℰ𝑟𝑒𝑐
− = {(𝑢, 𝑣) ∈ ℰ|𝑠𝑣𝑢 = −1 ∧ 𝑠𝑢𝑣 = −1 } (10)
Where, 𝑟1 is Unpreciprocated Trust, 𝑟2 is Unpredicted Distrust, 𝑟3 Recevied Trust, 𝑟4 is Received
Distrust,𝑟5is Mutual Trust and 𝑟6 is Mutual Distrust.
The sets form a partition: ⋃ 𝑟𝑖
6
𝑖=1 = ℰ and 𝑟𝑖 ∩ 𝑟𝑗 = ∅ for 𝑖 ≠ 𝑗. The relation-specific
neighborhood is 𝑁𝑟𝑖
(𝑢) = { 𝑣|(𝑢, 𝑣) ∈ 𝑟𝑖
}.
Relations 𝑟1 − 𝑟4 are from the SDGNN’s four SDRs. Relations 𝑟5 and 𝑟6 are novel for the ASRAGNN. It has been put in place by social exchange theory [10], which states that mutual trust (𝑟5 )
creates a qualitatively stronger and more stable social bond than two independent unilateral trust
edges: 𝑟5 represents confirmed friendship and is the main indication of friend recommendation.
𝑟5 represents a distinct relation type that helps ASRA-GNN to learn a different aggregation
message for confirmed mutual relationships. Similarly, 𝑟6 represents a confirmed structural
conflict that should propagate differently from one-sided distrust

3.1.3. Edge Weight Initialization for Binary-Sign Datasets

For datasets without explicit ratings, weights are initialized from three topological features and
refined end-to-end:
𝑤𝑢𝑣
(0) = 𝜎 (𝑀𝐿𝑃𝑤(𝑓𝑟𝑒𝑐(𝑢, 𝑣), 𝑓𝑗𝑎𝑐(𝑢, 𝑣), 𝑓𝑑𝑒𝑔(𝑢, 𝑣), 𝑠𝑢𝑣)) (11)

Where:

3.2. Signed Graph-Theoretic Edge Feature Vector

A central design principle of ASRA-GNN is that every edge (𝑢, 𝑣) ∈ ℰ carries richer information
than its sign 𝑠𝑢𝑣 and weight 𝑤𝑢𝑣 alone. We formalize a Signed Graph-Theoretic Edge Feature
Vector𝝆(𝑢, 𝑣) = [𝜌1, 𝜌2, 𝜌3, 𝜌4]⊤ ∈ ℝ4 encoding four structural properties, each grounded in a
distinct social network theory. This replaces SiGAT’s38 motifs at 𝒪(|ℰ| ⋅ 𝑎𝑣𝑔_𝑑𝑒𝑔)
precomputation vs. 𝒪(𝑛^3)

Reciprocity Score (𝝆𝟏) − Social Exchange Theory [10]: Reciprocal ties are structurally
stronger and more durable than unilateral ties ones. A reciprocated trust edge carries
fundamentally different social meaning:

𝜌1 (𝑢, 𝑣) = 𝟙[(𝑣, 𝑢) ∈ ℰ+]

𝜌1 = 1 signals (𝑢, 𝑣) ∈ 𝑟5 (mutual trust), warranting higher aggregation weight as a stable,
confirmed relationship.

Triadic Closure Score (𝝆𝟐) − Triadic Closure Theorem [12]: A tie is formed between two
nodes; it represents that they share a common positive neighbor. The Jaccard coefficient of
positive out-neighborhoods quantifies this:

Higher 𝜌2 indicates shared community membership, which directly captures the friend-of-friend
principle underlying friend recommendation.
Sign Consistency Score (𝝆𝟑) − Cognitive Dissonance Theory [13]: The structural information
of edges that are consistent with balance theory predictions is different from that of theoryviolating edges. Let 𝑠̂𝑢𝑣 denote the sign predicted by balance theory from observed 2-hop paths:

𝜌3(𝑢, 𝑣) = 𝟙[𝑠̂𝑢𝑣 = 𝑠𝑢𝑣]

𝜌3 = 0 flags a balance theory violation, directly informing the LATM gate (Section 3.4): nodes
with many 𝜌3 = 0 neighbors will learn low 𝜆𝑢, reducing reliance on theory-guided routing.

Status Differential Score (𝝆𝟒) − Status Theory [6]: Edge direction encodes social hierarchy:
𝑢 →+ 𝑣 means 𝑢 endorses 𝑣 as having a higher status. We operationalize this as a normalized
learned differential:

Where 𝑠𝑢 = 𝒘𝑠𝑡𝑎𝑡 ⊤ 𝒆𝑢 ∈ ℝ is a learned scalar status score, and 𝜎𝑠
is the standard deviation of status scores across 𝒱. Unlike 𝜌1 − 𝜌3 which are precomputed once, 𝜌4 is dynamic: as
embeddings evolve, status scores update and attention weights adapt accordingly, making status
theory an active trainable component of the attention mechanism.

3.3. Sign-Aware Structural Role Attention Encoder (SSRA)
The SSRA encoder is built on LightSGCN’s simplified propagation paradigm that has no weight
matrices 𝑾, no nonlinear activations 𝜎 in propagation. It works on pure neighborhood

aggregation with layer combination. The central novelty is replacing LightSGCN’s fixed
symmetric degree normalization 1/ (√|𝑁+(𝑢)| ⋅ √|𝑁+(𝑣)|) with a learned attention weight
derived from 𝝆(𝑢, 𝑣).

3.3.1. Node Embedding Initialization
Each node 𝑢 ∈ 𝒱 is associated with two learnable 𝑑 −dimensional vectors:
𝑒𝑢+, 𝑒𝑢− ∈ ℝ𝑑, initialized Xavier uniform (16)
The positive embedding channel captures 𝑢’s trust-based social identity and the negative
embedding channel captures 𝑢’s distrust-based social identity. Separate channels allows the
ASRA-GNN to follow balance theory’s distinction between trust and distrust networks

3.3.2. Attention Score Derivation
The ASRA-GNN derives the attention weight 𝛼(𝑢, 𝑣) in four steps, which is motivated by key
design asymmetry that positive edges should attend based on embedding similarity (homophily)
and negative edges should attend based on structural role contrast. A single formulation cannot
capture both, motivating the sign-aware gate.

Step 1 − Content-based attention (from GAT [5]):
𝑒𝑐(𝑢, 𝑣) = LeakyReLU(𝒂⊤|𝒆𝑢||𝒆𝑣|)
where 𝒂 ∈ ℝ2𝑑is learnable and 𝒆𝑢 = [𝑒𝑢+||𝑒𝑢−] ∈ ℝ2𝑑

Step 2 − Structural role attention (novel):

where 𝑏 ∈ ℝ4 maps the four social-theoretic scores to a scalar. High 𝜌1 (reciprocity) increases
attention via exchange theory; high 𝜌2 (triadic closure) via closure theorem; high 𝜌3 (sign
consistency) via cognitive dissonance theory; 𝜌4 modulates by hierarchical distance via status
theory. The learnable 𝒃 allows the ASRA-GNN to weight these four theories for the dataset at
hand.

Step 3 − Sign-aware gate (novel):

g(𝑢, 𝑣) = 𝜎(𝑐 ⋅ 𝑠𝑢𝑣 + 𝑑), 𝑐, 𝑑 ∈ ℝ learnable

For 𝑠𝑢𝑣 = +1: 𝑔 → 𝜎(𝑐 + 𝑑); for 𝑠𝑢𝑣 = −1: 𝑔 → 𝜎(−𝑐 + 𝑑). When 𝑐 > 0 and 𝑑 ≈ 0, positive
edges yield 𝑔 > 0.5 (content dominates) and negative edges yield 𝑔 < 0.5 (structural role
dominates).
This helps the theoretical asymmetry by spreading trust along paths that are similar to the ones
that are embedded and spreading distrust along the paths that are structurally different. No
previously signed GNN establishes the sign-dependent differentiation.

Step 4 − Combined score and normalization:

Separate normalization per relation type 𝑟𝑖 ensures attention weights sum to 1 within each type,
preserving interpretability of each relation-specific aggregation.

3.3.3. LightSGCN-Style Propagation with SSRA Weights
We proceed by decomposing ℰ into six mutually exclusive and collectively exhaustive relation
types, extending SDGNN’s four SDRs [7] with two Following LightSGCN [8] and LightGCN
[9], propagation contains no weight matrices and no nonlinear activations. Balance theory
governs sign routing: the positive channel 𝑒𝑢 aggregates from balanced paths (+, + and −, −);
the negative channel 𝑒𝑢− aggregates from unbalanced paths (+, − and −, +). The key departure
from LightSGCN is replacing the fixed normalization with 𝛼𝑟𝑖(𝑢, 𝑣) ⋅ 𝑤𝑢𝑣.
Positive channel (balanced path aggregation)

Negative channel (unbalanced path aggregation):

.

The balance theory routing derives from Heider’s consistency principle [2]: a (+, +) path (friendof-friend) and a (−, −) path (enemy-of-enemy) both yield a positive channel contribution. The
weight 𝑤𝑢𝑣 scales each message by continuous trust strength which is a path (+0.9, +0.8) that
contributes 4 × more than a path (+0.2, +0.3), even though both are theoretically equivalent
binary balance theory paths.

3.3.4. Message Passing and Signed Aggregation

ASRA-GNN follows the general GNN message-passing paradigm: for each node 𝑢, compute a
message per incoming edge, aggregate messages per channel, and update the node representation.
The unified message function for neighbor𝑣 to node 𝑢 under relation 𝑟𝑖 at layer 𝑙 is:

𝑚𝑟𝑖(𝑣 → 𝑢) = 𝛼𝑟𝑖(𝑢, 𝑣) ⋅ 𝑤𝑢𝑣 ⋅ 𝑒𝑣(𝑙)

where, 𝛼𝑟𝑖(𝑢, 𝑣) is the structural importance, 𝑤𝑢𝑣 is the trust strength and 𝑒𝑣(𝑙)is the neighbor
state.The three factors are separated. 𝛼𝑟𝑖(𝑢, 𝑣) is the SSRA attention weight encoding structural role
(who matters); 𝑤𝑢𝑣 ∈ (0,1] is the continuous trust weight (how strongly to believe this edge);
and 𝒆𝑣(𝑙 )is the neighbor’s current representation (what to propagate). Together, they are designed
to replace LightSGCN’s single fixed coefficient 1/ (√|𝑁+(𝑢)| ⋅ √|𝑁+(𝑣)|) with a learned,
theory-grounded, trust-scaled weight per relation type.Messages are aggregated per channel following balance theory’s sign routing rule [2]: balancedpaths (+, + and −, −) route to the positive channel; unbalanced paths (+, − and −, +) route to
the negative channel. No weight matrices or nonlinear activations are applied during aggregation,
following LightSGCN [8] and LightGCN [9].Positive channel (balanced path aggregation):