Square lattice network

- The network has a planar square lattice structure, and we are interested in the directed connectivity of any two points which both locate at intersection.
- The connectivity is affected by two factors. First, the Manhattan distance between the two point, and it is determined by the size of the lattice which is determined by the two points. For example, if there are 3 layers of horizontal edges and 2 layers of vertical edges between the two points, we will then look at the connectivity of a lattice network with size 3*2.
- The second factor is the connectivity of each single edge between any two adjacent intersections, denoted as p. For simplicity, we consider all edges have the same bond probability p.
- For a short demo below, you can enter the size of the lattice network and the connectivity probability could be calculated using our algorithm described in the paper[1]. By specifying the exact value of p, the connectivity of the lattice network could be calculated as well.

**Reference:** [1]. **Lei Zhang**, Lin Cai, Jianping Pan. "Connectivity in Two-Dimensional Lattice Networks", to appear in IEEE International Conference on Computer Communications (INFOCOM 2013), Turin, Italy, 14-19 Apr. 2013.

Lattice length:

The connectivity polynomial of the lattice is:

Bond connectivity p:

The lattice connectivity probability is:

Acknowledgment: This demo is a collaboration with Ph.D. student Fei Tong --- special thanks to him.