Optimization Models
Home
Software
Links
Index
Contact
1. Introduction
1.1. Overview
1.2. Optimization Models
2. Linear Algebra
2.1. Vectors
2.2. Matrices
2.3. Linear Equations
2.4.  Least-Squares
2.5. Eigenvalues
2.6  Singular Values
3. Convex Models
3.1. Convexity
3.2. LP and QP
3.3. SOCP
3.4. Robust LP
3.5. GP
3.6. SDP
3.7. Non-Convex Models
4. Duality
4.1. Weak Duality
4.2. Strong Duality
4.3.  Applications
5. Case Studies
5.1. Senate Voting
5.2. Antenna Arrays
5.3. Localization
5.4. Circuit Design

Rank properties of the arc-node incidence matrix

Recall the definition of the arc-node incidence matrix of a network.

A number of topological properties of a network with m nodes and n edges can be inferred from those of its node-arc incidence matrix A, and of the reduced incidence matrix tilde{A}, which is obtained from A by removing its last row. For example, the network is said to be connected if there is a path joining any two nodes. It can be shown that the network is connected if and only if the rank of tilde{A} is equal to m-1.

See also: Nullspace of a transpose incidence matrix.