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If you are determined to have an automated method, you can find
neighbors using <a moz-do-not-send="true"
href="https://gis.stackexchange.com/a/418824/4449">this approach.</a><br>
Then look for counties with no neighbors. For these counties look
for the closest counties in the same state and add these to the
list. <br>
<br>
But that seems like a lot of work for a small problem. A cursory
search suggests the number of island counties is quite small and you
can patch up the data by hand:
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<h2 data-path-to-node="2">1. <span
class="citation-7 citation-end-7">Hawaii (All 5 Counties)</span></h2>
<p data-path-to-node="3">As the only state located entirely on
an archipelago, all its counties are island-based.</p>
<ul data-path-to-node="4">
<li>
<p data-path-to-node="4,0,0"><b data-path-to-node="4,0,0"
data-index-in-node="0">Hawaii County:</b> The "Big
Island."</p>
</li>
<li>
<p data-path-to-node="4,1,0"><b data-path-to-node="4,1,0"
data-index-in-node="0">Honolulu County:</b> Oahu and
the Northwestern Hawaiian Islands.</p>
</li>
<li>
<p data-path-to-node="4,2,0"><b data-path-to-node="4,2,0"
data-index-in-node="0">Kalawao County:</b> A small
peninsula on Molokai (the smallest county in the US).</p>
</li>
<li>
<p data-path-to-node="4,3,0"><b data-path-to-node="4,3,0"
data-index-in-node="0">Kauai County:</b> Kauai,
Niihau, and others.</p>
</li>
<li>
<p data-path-to-node="4,4,0"><b data-path-to-node="4,4,0"
data-index-in-node="0">Maui County:</b> Maui, Lanai,
Molokai, and Kahoolawe.</p>
</li>
</ul>
<h2 data-path-to-node="5">2. Washington (2 Counties)</h2>
<p data-path-to-node="6">While most of Washington is on the
mainland, its northwestern corner is home to:</p>
<ul data-path-to-node="7">
<li>
<p data-path-to-node="7,0,0"><b data-path-to-node="7,0,0"
data-index-in-node="0">Island County:</b> Comprised
primarily of Whidbey and Camano Islands.</p>
</li>
<li>
<p data-path-to-node="7,1,0"><b data-path-to-node="7,1,0"
data-index-in-node="0">San Juan County:</b> Comprised
of the 170+ islands that make up the San Juan
archipelago.</p>
</li>
</ul>
<h2 data-path-to-node="8">3. Massachusetts (2 Counties)</h2>
<ul data-path-to-node="9">
<li>
<p data-path-to-node="9,0,0"><b data-path-to-node="9,0,0"
data-index-in-node="0">Nantucket County:</b>
Coextensive with Nantucket Island and its tiny neighbors
(Tuckernuck and Muskeget).</p>
</li>
<li>
<p data-path-to-node="9,1,0"><b data-path-to-node="9,1,0"
data-index-in-node="0">Dukes County:</b> Comprised of
Martha's Vineyard and the Elizabeth Islands.</p>
</li>
</ul>
<h2 data-path-to-node="10">4. New York (2 Counties)</h2>
<p data-path-to-node="11">Technically, two of New York City's
boroughs are their own island counties:</p>
<ul data-path-to-node="12">
<li>
<p data-path-to-node="12,0,0"><b
data-path-to-node="12,0,0" data-index-in-node="0">Richmond
County (Staten Island):</b> Comprised of Staten Island
and surrounding smaller islets.</p>
</li>
<li>
<p data-path-to-node="12,1,0"><b
data-path-to-node="12,1,0" data-index-in-node="0">New
York County (Manhattan):</b> Comprised of Manhattan
Island, Roosevelt Island, and others. (Note: A tiny 0.1
sq mile neighborhood called <b
data-path-to-node="12,1,0" data-index-in-node="136">Marble
Hill</b> is physically on the mainland due to a canal
being dug in 1895, but it remains legally part of the
island county).</p>
</li>
</ul>
<h2 data-path-to-node="13">5. Rhode Island (1 County)</h2>
<ul data-path-to-node="14">
<li>
<p data-path-to-node="14,0,0"><b
data-path-to-node="14,0,0" data-index-in-node="0">Newport
County:</b> While some of its towns are on the
mainland, the county itself is largely defined by <b
data-path-to-node="14,0,0" data-index-in-node="101">Aquidneck
Island</b>, <b data-path-to-node="14,0,0"
data-index-in-node="119">Conanicut Island</b>, and <b
data-path-to-node="14,0,0" data-index-in-node="141">Prudence
Island</b>. However, it is often excluded from
"entirely island" lists because a portion of the county
(the town of Little Compton and Tiverton) is physically
attached to the Massachusetts mainland.</p>
</li>
</ul>
<h2 data-path-to-node="15">6. Florida (1 County*)</h2>
<ul data-path-to-node="16">
<li>
<p data-path-to-node="16,0,0"><b
data-path-to-node="16,0,0" data-index-in-node="0">Monroe
County:</b> This is a "hybrid" case. While the
populated <b data-path-to-node="16,0,0"
data-index-in-node="60">Florida Keys</b> are entirely
islands, the county boundaries actually extend onto the
mainland to include a large, uninhabited portion of the
Everglades.</p>
</li>
</ul>
</div>
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