Pensieve header: Experiments with graph layouts.

Table[l->EG[VPB[3,(Subscript[σ, 2,3]),(Subscript[σ, 1,3]),(Subscript[σ, 3,1]),(Subscript[σ, 1,3]),(Subscript[σ, 3,1]),(Subscript[σ, 1,3])],GraphLayout->l],
{l,{"BipartiteEmbedding", "CircularEmbedding", "CircularMultipartiteEmbedding","DiscreteSpiralEmbedding","GridEmbedding","LinearEmbedding","MultipartiteEmbedding","SpiralEmbedding","StarEmbedding","BalloonEmbedding","RadialEmbedding","LayeredDigraphEmbedding","LayeredEmbedding","GravityEmbedding","HighDimensionalEmbedding","PlanarEmbedding","SpectralEmbedding","SpringElectricalEmbedding","SpringEmbedding","TutteEmbedding"}}
]

g//FullForm

Show[g, GraphLayout->"SpringElectricalEmbedding"]

Table[l->EG[BR[8,{1,3,5,7}],GraphLayout->l],
{l,{"BipartiteEmbedding", "CircularEmbedding", "CircularMultipartiteEmbedding","DiscreteSpiralEmbedding","GridEmbedding","LinearEmbedding","MultipartiteEmbedding","SpiralEmbedding","StarEmbedding","BalloonEmbedding","RadialEmbedding","LayeredDigraphEmbedding","LayeredEmbedding","GravityEmbedding","HighDimensionalEmbedding","PlanarEmbedding","SpectralEmbedding","SpringElectricalEmbedding","SpringEmbedding","TutteEmbedding"}}
]