graphs=RandomGraph[UniformGraphDistribution[10,20],104];

Histogram[VertexDegree[#,1]&/@graphs]

graphs=RandomGraph[BernoulliGraphDistribution[10,0.7],104];

Histogram[VertexDegree[#,1]&/@graphs]

graphs=RandomGraph[BarabasiAlbertGraphDistribution[500,3]];

Histogram[VertexDegree[graphs],{"Log",10}]

graphs=RandomGraph[PriceGraphDistribution[103,3,1]];

Histogram[VertexDegree[graphs],{"Log",10}]