Scale-free networks are prevalent in cellular biology, reflecting the complex interactions among cellular components such as DNA, RNA, proteins, and small molecules. These interactions are coordinated through signaling pathways and regulatory mechanisms, enabling cells to respond to environmental changes. Recent theoretical advances allow the use of graph concepts to describe cellular network structures, revealing features shared with non-biological networks. Understanding cellular network topology is crucial for elucidating their function and dynamics. Cellular networks can be represented as graphs, where nodes are components and edges are interactions. Key graph properties include node degree, clustering coefficient, and path length. Scale-free networks exhibit a power-law degree distribution, indicating a high diversity of node degrees with no typical node. Clustering coefficients vary with node degree, showing that low-degree nodes tend to be in highly cohesive neighborhoods, while high-degree nodes have less connected neighbors. Various cellular networks, including protein interaction and metabolic networks, display scale-free properties. These networks have a small-world property, with short path lengths between nodes. Directed graphs have special features, such as strongly connected components, in-components, and out-components, reflecting functional separation in signal transduction and metabolic networks. Several graph models have been developed to understand network organization. Growing network models, such as those with preferential attachment, generate scale-free degree distributions. Scale-free random graphs have smaller path lengths than random graphs and similar local cohesiveness. Protein interaction networks and metabolic networks exhibit scale-free properties, with degree distributions following power laws. Genomic and proteomic data have revealed the topology of specific cellular networks, such as protein interaction networks and metabolic networks. These networks show scale-free properties, with a degree distribution following a power law. The clustering-degree function varies with node degree, indicating heterogeneous clustering. Transcriptional regulatory networks also exhibit scale-free properties, with approximately scale-free out-degree distributions. In-degree distributions are more restricted, indicating that combinatorial regulation is less common than regulation by a single transcription factor. Signal transduction networks are highly interconnected, with a large strongly connected component. These networks have short path lengths, enabling rapid responses to signaling inputs. The in- and out-degree distributions follow power-law exponents, indicating the presence of highly connected nodes. Functional association networks, based on gene co-expression, gene fusion, or genetic interactions, have also been constructed. These networks show small-world and scale-free properties, with short path lengths and power-law degree distributions. The architectural features of molecular interaction networks are shared with other complex systems, such as technological and social networks. However, the functional and evolutionary constraints of cellular networks must be considered when interpreting graph properties. Hubs in scale-free networks are highly connected nodes that are critical for network function. The loss of hubs can lead to network breakdown, highlighting their importance. Essential genes are often highly connected, indicating their role in cellular robustness. Modularity in cellular networks refers to the presence of functionally separable subnetworks. However, modules often overlap, with high cross-talkScale-free networks are prevalent in cellular biology, reflecting the complex interactions among cellular components such as DNA, RNA, proteins, and small molecules. These interactions are coordinated through signaling pathways and regulatory mechanisms, enabling cells to respond to environmental changes. Recent theoretical advances allow the use of graph concepts to describe cellular network structures, revealing features shared with non-biological networks. Understanding cellular network topology is crucial for elucidating their function and dynamics. Cellular networks can be represented as graphs, where nodes are components and edges are interactions. Key graph properties include node degree, clustering coefficient, and path length. Scale-free networks exhibit a power-law degree distribution, indicating a high diversity of node degrees with no typical node. Clustering coefficients vary with node degree, showing that low-degree nodes tend to be in highly cohesive neighborhoods, while high-degree nodes have less connected neighbors. Various cellular networks, including protein interaction and metabolic networks, display scale-free properties. These networks have a small-world property, with short path lengths between nodes. Directed graphs have special features, such as strongly connected components, in-components, and out-components, reflecting functional separation in signal transduction and metabolic networks. Several graph models have been developed to understand network organization. Growing network models, such as those with preferential attachment, generate scale-free degree distributions. Scale-free random graphs have smaller path lengths than random graphs and similar local cohesiveness. Protein interaction networks and metabolic networks exhibit scale-free properties, with degree distributions following power laws. Genomic and proteomic data have revealed the topology of specific cellular networks, such as protein interaction networks and metabolic networks. These networks show scale-free properties, with a degree distribution following a power law. The clustering-degree function varies with node degree, indicating heterogeneous clustering. Transcriptional regulatory networks also exhibit scale-free properties, with approximately scale-free out-degree distributions. In-degree distributions are more restricted, indicating that combinatorial regulation is less common than regulation by a single transcription factor. Signal transduction networks are highly interconnected, with a large strongly connected component. These networks have short path lengths, enabling rapid responses to signaling inputs. The in- and out-degree distributions follow power-law exponents, indicating the presence of highly connected nodes. Functional association networks, based on gene co-expression, gene fusion, or genetic interactions, have also been constructed. These networks show small-world and scale-free properties, with short path lengths and power-law degree distributions. The architectural features of molecular interaction networks are shared with other complex systems, such as technological and social networks. However, the functional and evolutionary constraints of cellular networks must be considered when interpreting graph properties. Hubs in scale-free networks are highly connected nodes that are critical for network function. The loss of hubs can lead to network breakdown, highlighting their importance. Essential genes are often highly connected, indicating their role in cellular robustness. Modularity in cellular networks refers to the presence of functionally separable subnetworks. However, modules often overlap, with high cross-talk