Using edge weights is essential for modeling real-world systems where links possess relevant information, and preserving this information in low-dimensional representations is relevant for classification and prediction tasks. This paper systematically investigates how different random walk strategies—traditional unweighted, strength-based, and fully weight-aware—keep edge weight information when generating node embeddings. Using network models, real-world graphs, and networks subjected to low-weight edge removal, we measured the correlation between original edge weights and the similarity of node pairs in the embedding space generated by random walk strategies. Our results consistently showed that weight-aware random walks significantly outperform other strategies, achieving correlations above 0.90 in network models. However, performance in real-world networks was more heterogeneous, influenced by factors like topology and weight distribution. Our analysis also revealed that removing weak edges via thresholding can initially improve correlation by reducing noise, but excessive pruning degrades representation quality. Our findings suggest that simply using a weight-aware random walk is generally the best approach for preserving edge weight information in embeddings, but it is not a universal solution.

Discovery processes have been an important topic in the network science field. The exploration of nodes can be understood as the knowledge acquisition process taking place in the network, where nodes represent concepts and edges are the semantical relationships between concepts. While some studies have analyzed the performance of the knowledge acquisition process in particular network topologies, here we performed a systematic performance analysis in well-known dynamics and topologies. Several interesting results have been found. Overall, all learning curves displayed the same learning shape, with different speed rates. We also found ambiguities in the feature space describing the learning curves, meaning that the same knowledge acquisition curve can be generated in different combinations of network topology and dynamics. A surprising example of such patterns are the learning curves obtained from random and Waxman networks: despite the very distinct characteristics in terms of global structure, several curves from different models turned out to be similar. All in all, our results suggest that different learning strategies can lead to the same learning performance. From the network reconstruction point of view, however, this means that learning curves of observed sequences should be combined with other sequence features if one aims at inferring network topology from observed sequences.

Complex networks have been found to provide a good representation of the structure of knowledge, as understood in terms of discoverable concepts and their relationships. In this context, the discovery process can be modeled as agents walking in a knowledge space. Recent studies proposed more realistic dynamics, including the possibility of agents being influenced by others with higher visibility or by their own memory. However, rather than dealing with these two concepts separately, as previously approached, in this study we propose a multi-agent random walk model for knowledge acquisition that incorporates both concepts. More specifically, we employed the true self avoiding walk alongside a new dynamics based on jumps, in which agents are attracted by the influence of others. That was achieved by using a L\'evy flight influenced by a field of attraction emanating from the agents. In order to evaluate our approach, we use a set of network models and two real networks, one generated from Wikipedia and another from the Web of Science. The results were analyzed globally and by regions. In the global analysis, we found that most of the dynamics parameters do not significantly affect the discovery dynamics. The local analysis revealed a substantial difference of performance depending on the network regions where the dynamics are occurring. In particular, the dynamics at the core of networks tend to be more effective. The choice of the dynamics parameters also had no significant impact to the acquisition performance for the considered knowledge networks, even at the local scale.

Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify the symmetries around nodes, which we call connectivity patterns. We develop two topological transformations that allow a concise characterization of the different types of symmetry appearing on networks and apply these concepts to six network models, namely the Erd\H{o}s-R\'enyi, Barab\'asi-Albert, random geometric graph, Waxman, Voronoi and rewired Voronoi. Real-world networks, namely the scientific areas of Wikipedia, the world-wide airport network and the street networks of Oldenburg and San Joaquin, are also analyzed in terms of the proposed symmetry measurements. Several interesting results emerge from this analysis, including the high symmetry exhibited by the Erd\H{o}s-R\'enyi model. Additionally, we found that the proposed measurements present low correlation with other traditional metrics, such as node degree and betweenness centrality. Principal component analysis is used to combine all the results, revealing that the concepts presented here have substantial potential to also characterize networks at a global scale.