IndexedFactorGraphs

A Julia package to work with factor graphs.

Installation

julia> using Pkg; Pkg.add("IndexedFactorGraphs")

Basics

A factor graph is a set of variable and factor vertices connected by edges. In the spirit of IndexedGraphs.jl, here each edge comes with an index, which can be used to access edge properties (e.g. messages in a message-passing algorithm).

Graph construction

A FactorGraph can be constructed starting from an adjacency matrix, with the convention that rows represent factor vertices and columns represent variable vertices

julia> using IndexedFactorGraphs

julia> g = FactorGraph([0 1 1 0;
                        1 0 0 0;
                        0 0 1 1])
FactorGraph{Int64} with 4 variables, 3 factors, and 5 edges

Alternatively, use one of the provided generators for random factor graphs

julia> g_rand = rand_factor_graph(5, 3, 6)
FactorGraph{Int64} with 5 variables, 3 factors, and 6 edges

Graph navigation

Given a factor graph with $N$ variables and $M$ factors, variables are indexed by $i\in{1,\ldots,N}$, factors are indexed by $a\in{1,\ldots,M}$. Properties of a vertex can be queried by wrapping the vertex index in a variable or factor. For example, the list of neighbors of variable $i=2$ is found by

julia> ∂i = neighbors(g, variable(2));

julia> collect(∂i)
2-element Vector{Int64}:
 1
 3

where $1,3$ are to be interpreted as indices of factor vertices.

The list of edges adjacent to factor $a=1$ is found by

julia> ea = inedges(g, factor(1));

julia> collect(ea)
3-element Vector{IndexedGraphs.IndexedEdge{Int64}}:
 Indexed Edge 1 => 1 with index 1
 Indexed Edge 2 => 1 with index 2
 Indexed Edge 5 => 1 with index 6

Querying properties of a vertex without specifying whether it's a variable or a factor will throw an error

julia> outedges(g, 3)
ERROR: ArgumentError: Properties of a vertex of an `AbstractFactorGraph` such as degree, neighbors, etc. cannot be accessed by an integer. Use a `variable` or `factor` wrapper instead.

See also

For less lightweight implementations, also including message-passing algorithms, check out

• FactorGraph.jl
• ForneyLab.jl