Diffusion on a Directed Network, General VersionThis model demonstrates diffusion of a quantity through a directed network. The quantity moves among nodes in the network only along established, directed links between two nodes. The simple rules that drive this diffusion lead to interesting patterns related to the topology, density, and stability of the network. Furthermore, the model may be useful in understanding the basic properties of dynamic processes on networks, and provides a useful starting point for designing more complex and realistic network-based models. In this version nodes can be connected to connected to any other node in the network. The d3 force-directed graph layout used to display this network provides a robust environment for viewing the simulation; for example, to view a particular node just drag it away from its neighbors to an empty area of the view. HOW IT WORKSIn each tick, each node shares some percentage (defined by the rate slider) of its "value" quantity with its neighbors in the network. Specifically, flow from node A to node B occurs only if there is a directed link from A to B and A has more value than B. The amount of flow is proportional to the difference between the value of A and the value of B, and the strength of the link from A to B. If a node has no outgoing links, then it doesn't share any of it's value; it just accumulates any that its neighbors have provided via incoming links. Note that because it is a directed network, node A may give value to node B even if node B doesn't give back.The size and color of each node shows how much "value" that node has, where the area of the node is proportional to its value. The strength of a link is indicated by its stroke width. During the simulation active links turn magenta with color intensity proportional to amount of flow. Hovering the mouse over either a node or link produces a tooltip respectively showing the current value of the node or flow through the link. The Total Value field demonstrates that value is conserved throughout the simulation. The Flow (Root Mean Square) field shows the root mean square of the flow between nodes at each time step. Note that this value decreases to 0. With each reset a new network, containing the number of nodes indicated by the Number of Nodes slider, is configured with the probability of a link between any node pair given by the Connection Probability slider. (Note: in order to create an easily viewed network, we recommend that this value be selected so that the number of links to each node averages no more than 5). Based on: Stonedahl, F. and Wilensky, U. (2008). NetLogo Diffusion on a Directed Network model. http://ccl.northwestern.edu/netlogo/models/DiffusiononaDirectedNetwork. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. |