Network science has become a powerful tool to describe the structure and dynamics of real-world complex physical, biological, social, and technological systems. Largely built on empirical observations to tackle heterogeneous, temporal, and adaptive patterns of interactions, its intuitive and flexible nature has contributed to the popularity of the field. With pioneering work on the evolution of random graphs, graph theory is often cited as the mathematical foundation of network science. Despite this narrative, the two research communities are still largely disconnected. In this commentary, we discuss the need for further cross-pollination between fields – bridging the gap between graphs and networks – and how network science can benefit from such influence. A more mathematical network science may clarify the role of randomness in modeling, hint at underlying laws of behavior, and predict yet unobserved complex networked phenomena in nature. What is the path towards a physical theory of complex networked systems? With an eye to the historical maths-physics duality, and an outlook towards the future, this commentary discusses promises and challenges accompanying the convergence of formal graph theory and data-inspired network science.

中文翻译：

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缩小图和网络之间的差距

网络科学已经成为描述现实世界中复杂的物理，生物，社会和技术系统的结构和动力学的强大工具。其直观和灵活的特性很大程度上建立在基于经验观察的基础上，以解决交互的异构，时间和适应性模式，从而促进了该领域的普及。随着关于随机图进化的开拓性工作，图论经常被引用为网络科学的数学基础。尽管有这样的叙述，但两个研究社区仍然很大程度上脱节。在这篇评论中，我们讨论了领域之间进一步交叉授粉的必要性–弥合图与网络之间的鸿沟–以及网络科学如何从这种影响中受益。更加数学化的网络科学可能会阐明随机性在建模中的作用，暗示行为的基本规律，并预测自然界中尚未发现的复杂网络现象。走向复杂网络系统的物理理论的途径是什么？着眼于历史上的数学-物理学的二元性，以及对未来的展望，本评论讨论了形式图论与数据启发型网络科学融合带来的希望和挑战。