Social networks are a key concept in mathematical sociology, representing the connections and interactions between individuals or groups.

The degree of a node in a social network is the number of edges connected to it, representing the number of connections or interactions the node has.

Density is a measure of the interconnectedness of a social network, calculated as the ratio of the number of actual edges to the number of possible edges.

A Nash equilibrium in game theory is a set of strategies where no player can improve their outcome by changing their strategy, assuming other players' strategies remain unchanged.

Social Network Theory emphasizes the role of social networks in shaping individual behavior and outcomes, focusing on the influence of network structure and relationships on individual attitudes, beliefs, and actions.

Homophily is the tendency for individuals to form connections with others who are similar to them, often based on shared characteristics such as age, gender, race, or social status.

Diffusion models are mathematical models used to represent the spread of information or influence through a social network, capturing the dynamics of how individuals adopt new ideas or behaviors based on their connections with others.

The clustering coefficient of a node in a social network is the ratio of actual edges to possible edges in the node's neighborhood, measuring the extent to which the node's neighbors are connected to each other.

Social Network Analysis is a mathematical technique used to identify patterns and relationships in social network data, examining the structure and dynamics of social networks to understand how they influence individual and group behavior.

The diameter of a social network is the longest path between any two nodes in the network, representing the maximum distance between any two individuals in the network.

Game Theory models are mathematical models used to represent the behavior of rational actors in strategic situations, where each actor's actions affect the outcomes of others, capturing the dynamics of decision-making and strategic interactions.

The average path length in a social network is the average distance between all pairs of nodes in the network, measuring the overall connectivity and efficiency of the network.

Principal Component Analysis is a mathematical technique used to reduce the dimensionality of social network data while preserving important information, identifying the most significant patterns and relationships in the data.

Structural holes in a social network are nodes that bridge different parts of the network, acting as connectors between otherwise disconnected groups or individuals.

Opinion Dynamics models are mathematical models used to represent the dynamics of opinion formation and change in a social network, capturing how individuals' opinions evolve over time based on their interactions with others.