Thank you all for the helpful reviews. "and the goal is to figure out what type of object each pixel corresponds to" [Forouzan, 2015]. As suggested, we will run and report experiments on more networks, for a more comprehensive picture of our algorithm. We will focus more on the real-world networks. Segmentation-11 details... See above section on experiments .

Identifying influential nodes in complex networks is a critical task with a wide range of applications across different domains. However, existing approaches often face trade-offs between accuracy and computational efficiency. To address these challenges, we propose 1D-CGS, a lightweight and effective hybrid model that integrates the speed of one-dimensional convolutional neural networks (1D-CNN) with the topological representation power of GraphSAGE for efficient node ranking. The model uses a lightweight input representation built on two straightforward and significant topological features: node degree and average neighbor degree. These features are processed through 1D convolutions to extract local patterns, followed by GraphSAGE layers to aggregate neighborhood information. Experimental evaluations on twelve real world networks demonstrate that 1D-CGS significantly outperforms traditional centrality measures and recent deep learning models in ranking accuracy, while operating in very fast runtime. The proposed model achieves an average improvement of 4.73% in Kendall's Tau correlation and 7.67% in Jaccard Similarity over the best performing deep learning baselines. It also achieves an average Monotonicity Index (MI) score 0.99 and produces near perfect rank distributions, indicating highly unique and discriminative rankings. Furthermore, all experiments confirm that 1D-CGS operates in a highly reasonable time, running significantly faster than existing deep learning methods, making it suitable for large scale applications.

Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for many agents often remain computationally infeasible and lack theoretical guarantees. Mean Field Games (MFGs) address both of these issues and can be extended to Graphon MFGs (GMFGs) to include network structures between agents. Despite their merits, the real world applicability of GMFGs is limited by the fact that graphons only capture dense graphs. Since most empirically observed networks show some degree of sparsity, such as power law graphs, the GMFG framework is insufficient for capturing these network topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which builds on the graph theoretical concept of graphexes. Graphexes are the limiting objects to sparse graph sequences that also have other desirable features such as the small world property. Learning equilibria in these games is challenging due to the rich and sparse structure of the underlying graphs. To tackle these challenges, we design a new learning algorithm tailored to the GXMFG setup. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery. After defining the system and providing a theoretical analysis, we state our learning approach and demonstrate its learning capabilities on both synthetic graphs and real-world networks. This comparison shows that our GXMFG learning algorithm successfully extends MFGs to a highly relevant class of hard, realistic learning problems that are not accurately addressed by current MARL and MFG methods.

Abstract-- We use multiple measures of graph complexity to evaluate the realism of synthetically-generated networks of human activity, in comparison with several stylized network models as well as a collection of empirical networks from the literature. The synthetic networks are generated by integrating data about human populations from several sources, including the Census, transportation surveys, and geographical data. The resulting networks represent an approximation of daily or weekly human interaction. Our results indicate that the synthetically generated graphs according to our methodology are closer to the real world graphs, as measured across multiple structural measures, than a range of stylized graphs generated using common network models from the literature. I. INTRODUCTION Artificially generated graphs benefit from high demand in several application domains, wherever the phenomena of interest are driven by interactions between people, including health and medicine, communications, the economy, and national security. Lack of access to appropriate network data hampers the research community's ability to develop algorithms toanalyze and gain insight from these transactional graph datasets. Due to the access restrictions to real network data, there is value in crafting methods of synthetically generated data which faithfully represent behaviors of real world processes. As such, many stylized methods for creating graphs with rigorously understood structural properties have been established, making collective steady progress towards better approximating structures of real world processes. Despite this progress, these relatively simple stylized methods aren't universally applicable and suffer from lack of realism for some applications. We are particularly interested in creating realistic graphs which represent a complex set of interrelated processes involving a common subset of actors (i.e., the coherent alignment of disparate subgraphs which have many vertices in common and which represent different types of underlying activity).

A group of computer scientists have built a machine learning algorithm that can sniff out fake profiles lurking on social networks. It's likely that you and your Facebook friends have the same mutual friends. And on Twitter, it's also probable that your followers also follow the same people you do too due to common interests. These associations in social networks can be modeled on a graph as edges, where users are the vertices or nodes. The researchers from the Ben-Gurion University of the Negev, Israel, and the University of Washington, United States, hunted for fake social media accounts by developing an unsupervised learning algorithm that measures the probability of an edge existing between vertices.

Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to sophisticated but computationally costly alignment-based approaches. Yet it remains challenging to accurately cluster networks that are of a different size and density, but hypothesized to be structurally similar. In this paper, we address this problem by introducing a new network comparison methodology that is aimed at identifying common organizational principles in networks. The methodology is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.