Probabilistic Graph Theory

Probabilistic Graph Theory studies networks (graphs) where connections between elements (nodes) are determined by probability. Instead of fixed links, each possible connection has a chance of existing, allowing mathematicians to analyze typical properties and behaviors of random networks. This approach helps understand complex systems like social networks, communication systems, or biological networks by predicting how likely certain structures or patterns are to occur. It combines graph theory with probability, providing insights into the randomness and structure inherent in many real-world systems.