An Empirical Method for the Evaluation of Dynamic Network Simulation Methods Daniel P. Baller, Joshua Lospinoso, and Anthony N. Johnson Department of Mathematics, United States Military Academy, West Point, NY, USA Abstract - Real world communication networks are dynamic, thus reliably estimating network measures is challenging. Therefore a new framework is proposed to determine the underlying probability distribution of specific communication network measures. Communications between two individuals that are socially connected may vary, yet their underlying relationship remains unchanged. In this case, estimates of network measures, such as density or degree centrality may be severely affected by the occurrence or absence of observed communication between individuals. Two communication networks are modeled from empirical data using the network probability matrix (NPM). The NPM estimates the underlying edge probabilities between each pair of individuals. This framework can model a specific social group regardless of their network topology. Monte Carlo simulation is used with the NPM to generate instances of each communication network. A statistical distribution is fit to the density measure. This probability distribution can then be used to detect statistically significant changes in density. Keywords: NPM, Network Probability Matrix, Social Network, Density, Distribution 1 Introduction Presently many structure based frameworks are used in the network science community for the simulation of networks. These frameworks are based on the presence of triads, dyads, cliques and other network structural components. However theses frameworks do not always consider all of the factors that contribute to the dyadic relationship between agents. In a network an agent may not be interested in the occurrence of a triad between three other agents or that certain agents in the network have dyadic ties. The agent is mainly concerned with his or her own dyadic relationships leading to an underlying dynamic equilibrium in the network, i.e. the underlying edge probability structure that contains a probability that each agent will communicate with every other agent in the network. For an example of a dynamic equilibrium take a network of four agents. Within this network agent 1 has a 0.5 probability of communicating with agent 2, a 0.75 probability of communicating with agent 3, and a 0.0 probability of communicating with agent 4. These probabilities result from agent 1’s relationship with each other agent in the network and remain constant regardless of who agent 1 is communicating with at any given time. The underlying probability structure of a network remains independent of observations at any instance in time and is constant in the network. A single observation of communication does not necessarily designate a relationship between two agents, since the communication could have been made in error. On the other hand a single observation of the lack of communication does not designate that a relationship does not exist, since agents are not continuously communicating with every agent they have a relationship with at every instance in time. While a snapshot of the network at an instance in time does not indicate the dyadic relationships between agents, this snapshot is based on the underlying network probability that each agent will communicate with every other agent. A new framework is proposed for the simulation of networks that is based on the underlying probability structure of the dynamic equilibrium. This framework is the network probability matrix (NPM) proposed by McCulloh and Lospinoso (2007) [1]. The network probability matrix estimates the edge probabilities for each dyadic pair in the network. Probability estimation can vary from a proportion of communications in a series of observations or be estimated from more complex distributions depending on the amount and type of data present. This framework can be used to simulate a network regardless of its topology: random, small- world, scale free, cellular, ect. The edge probability structure of the underlying dynamic equilibrium remains constant in the network, while the network is at a stable state. However, the underlying probabilities may change as shocks to the network take place. A shock to the system can be caused by a variety of occurrences, such as two agents being assigned to work together on a project, the temporary absence of an agent from a network, or a change in leadership within an organization. Once a shock takes place the underlying probabilities of communication within the network will then stabilize as the network returns to it dynamic equilibrium. Using Monte Carlo simulation with the NPM the underlying distributions of network measures can be determined while the network is in its dynamic equilibrium. These underlying distributions can be used in change detection and allow us to statically predict shocks to the network and determine when significant changes occur.