- Chains

Consider a current distribution with *Ii* flowing along each edge *ei* ∈ E. Here, *ei* is directed and *Ii* flows in the direction of *ei*. A negative *Ii* represents a current flow in the reverse direction of *ei*. This current distribution can be represented by a formal sum *I* = ∑|E| *i*=1 *Ii ei*, where E generates a vector space over real numbers R. In a strict sense, we should consider RA := {*s*<sup>A</sup>|*s* ∈ R} with the unit of ampere A instead of R for a current distribution, but we omitted the unit to avoid notation complexity. A vector spanned by elements in E is called a 1*-chain*. The vector space composed of all 1-chains is denoted by *C*1. Similarly, we can define a 0*-chain* as ∑|N | *i*=1 *qini* with *qi* ∈ R, and introduce a vector space *C*0 over R as the totality of 0-chains.
