US States: Graph Representation

Construct a border-adjacency graph of US states and compare it with the built-in ContiguousUSAGraph

Construct the connectivity graph of the contiguous US states plus Washington, DC:

In[1]:=

Lengthcontusa=ComplementEntityList

all US states with District of Columbia

ADMINISTRATIVE DIVISIONS

,

Alaska, United States

ADMINISTRATIVE DIVISION

Hawaii, United States

ADMINISTRATIVE DIVISION



Out[1]=

Make a list of rules representing adjacent states:

In[2]:=

borderingrules=Flatten@KeyValueMap[Thread@*Rule,EntityValue[contusa,"BorderingStates","EntityAssociation"]];

Visualize the resulting graph:

In[3]:=

graph1=UndirectedGraph[Graph[contusa,borderingrules],VertexCoordinatesReverse/@EntityValue[contusa,"Coordinates"],VertexLabelsPlaced["Name",Tooltip]]

Out[3]=

Check the vertex and edge counts:

In[4]:=

Through[{VertexCount,EdgeCount}[graph1]]

Out[4]=

{49,111}

Compare with the counts for the ContiguousUSAGraph:

In[5]:=

GraphData["ContiguousUSAGraph",{"VertexCount","EdgeCount"}]

Out[5]=

{49,107}

Exclude four pairs of states that either share only a single point in common or have a sea border but no land border:

In[6]:=

exclude=

Arizona, United States

ADMINISTRATIVE DIVISION

Colorado, United States

ADMINISTRATIVE DIVISION

,

Michigan, United States

ADMINISTRATIVE DIVISION

Minnesota, United States

ADMINISTRATIVE DIVISION

,

New Mexico, United States

ADMINISTRATIVE DIVISION

Utah, United States

ADMINISTRATIVE DIVISION

,

New York, United States

ADMINISTRATIVE DIVISION

Rhode Island, United States

ADMINISTRATIVE DIVISION

;

Visualize the excluded borders:

In[7]:=

Function[pairs,GeoGraphics[Transpose[{{Blue,Red},Polygon[#]&/@pairs}]]]/@exclude

Out[7]=





Construct connectivity rules excluding these four edges:

In[8]:=

borderingrules2=Complement[borderingrules,Join[Rule@@@exclude,Rule@@@Reverse/@(exclude)]];

In[9]:=

graph2=UndirectedGraph[Graph[contusa,borderingrules2],VertexCoordinatesReverse/@EntityValue[contusa,"Coordinates"],VertexLabelsPlaced["Name",Tooltip]]

Out[9]=

Check the vertex and edge counts:

In[10]:=

Through[{VertexCount,EdgeCount}[graph2]]

Out[10]=

{49,107}

Verify this graph is isomorphic to the ContiguousUSAGraph using

ToEntity

In[11]:=

ToEntity[graph2]

Out[11]=

contiguous USA graph

Retrieve the built-in graph:

In[12]:=

GraphData[CanonicalName[%]]

Out[12]=

Verify the graph isomorphism above in another way:

In[13]:=

IsomorphicGraphQ[graph2,%]

Out[13]=

True

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Contributed by: Wolfram Staff

Wolfram Language Example Repository

US States: Graph Representation

See Also

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US States: Graph Representation

See Also

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