Random geometric graphs, formed as unit disk graphs with randomly generated disk centers, have also been used as a model of percolation and various other phenomena. ![]() If all nodes have transmitters of equal power, these circles are all equal. Node locations are modeled as Euclidean points, and the area within which a signal from one node can be received by another node is modeled as a circle. ![]() It is assumed that all nodes are homogeneous and equipped with omnidirectional antennas. In this application, nodes are connected through a direct wireless connection without a base station. One central node connected to seven leaves: if each of seven unit disks touches a common unit disk, some two of the seven disks must touch each other.īeginning with the work of Huson & Sen (1995), unit disk graphs have been used in computer science to model the topology of ad-hoc wirelessĬommunication networks. An example of a graph that is not a unit disk graph is the star K1,7 with In which two points are connected if their distance is below a fixed thresholdĮvery induced subgraph of a unit disk graph is also a unit disk graph. This generates 4 clusters of size 50 of radius 0.3 with centers chosen at random in the unit square. '''returns n random points in disk of radius r centered at c''' x,y c points. When you pass this function in the appropriate lists, one with the radius for each circle and the other with the desired number of points it returns a list of coordinate arrays, one for each circle. Two circles are connected by an edge if one circle contains the center of the other circleĪ graph formed from a collection of points in the Euclidean plane, Each cluster can be within a given set of x-y co ordinates. ![]() There are several possible definitions of the unit disk graph, equivalent to each other up to a choice of scale factor:Īn intersection graph of equal-radius circles, or of equal-radius disksĪ graph formed from a collection of equal-radius circles, in which That is, we form a vertex for each circle, and connect two vertices by an edge whenever the corresponding circles cross each other. In geometric graph theory, a unit disk graph is the intersection graph of a family of unit circles in the Euclidean plane. A collection of unit circles and the corresponding unit disk graph.
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