Shape irregularity of Life-Like Network Automaton rules as an indicator of classification performance

Complex Network (CN) classification requires high-level structural characterizations that are both scale-invariant and computationally efficient. Methods based on Life-Like Network Automata (LLNA) offer an interesting way to extract network descriptors by leveraging emergent temporal patterns without requiring provided features, but their efficacy is bottlenecked by a high-cost combinatorial optimization problem: the selection of the automaton transition rule. While current literature relies on exhaustive searches that are unfeasible for large-scale applications, this work reveals that the rule space is fundamentally structured by a property we term ``jaggedness'', that quantifies the resemblance of a LLNA transition function with a sawtooth shape. We demonstrate that this metric acts as a theoretical proxy for chaoticity and sensitivity -- properties essential for generating discriminative dynamic behaviors among network categories. Moreover, we introduce a heuristic search strategy that uses jaggedness to guide the rule selection. Experimental results show that our approach achieves classification accuracies within 5% of the global optimum while reducing computational overhead by 90% compared to exhaustive approach. Our findings provide a novel, efficient, framework for optimizing automata-based methods for pattern recognition.