Interstate Migration as a Chord
Diagram
Everybody moved, almost nobody left: a year of
state-to-state flows in one circle, and the grouping the circle
demands
Democracy’s Data
Last updated September 15, 2026 at 4:42p EDT
Americans tell the story of their own migration as an exodus. The
Northeast empties into the South, California empties into Texas, and
whole regions are winners or losers. The story matters to democracy
because House seats and electoral votes really do follow the movers. But
is the movement actually one-way? Or do the flows mostly run in both
directions at once and cancel?
The record that can answer this is a survey. In the year the American
Community Survey last measured it, 7,157,607 people in the United States
lived in a different state than they had lived in twelve months earlier.
Another 29,888,154 moved within their own state, and 2,552,193 arrived
from abroad. The between-state moves are published as a matrix: 52
origins by 52 destinations, 2,652 ordered pairs. Each pair carries an
estimate and a margin of error, which says how far off that estimate
could be.
That matrix is the cleanest flow data in American demography, and it
is almost impossible to look at. A chord diagram is the
form built for exactly this shape of data. It is a circle whose rim is
the set of places, with a ribbon joining each pair, wide where the flow
is heavy. It will not take 2,652 ribbons. Getting the matrix small
enough to draw is most of the work in this brief, and it is where the
arguing should happen.
The test
The flows are the Census Bureau’s State-to-State Migration
Flows table, from the 2024 American Community Survey one-year
estimates. The ACS reaches roughly 3.5 million addresses a year and asks
each household where it lived one year ago; that one question is the
country’s entire measurement of moving. The American Community Survey
chapter is the survey’s biography: who is in it, how it is weighted
up to the country, and why a margin of error stands beside every
estimate it publishes.
The numbers here are the same tables the migration brief hands over,
suppressed cells and all, so the two documents cannot silently disagree
about a number. The test itself is the one the exodus story begs for.
Group the states, add up the flow in each direction between every pair
of groups, and measure how much is net and how much cancels.
The data
One row of the flow table is an ordered pair of states. Direction is
a column, not a sign: Middle Atlantic to South Atlantic and South
Atlantic to Middle Atlantic are two different rows holding two different
numbers, and this brief turns on the fact that both are large.
| Middle Atlantic |
South Atlantic |
307,170 |
the larger direction |
| South Atlantic |
Middle Atlantic |
186,857 |
the smaller direction |
After grouping, the working table keeps six columns:
| from |
the group people left |
categorical |
| to |
the group they arrived in; when it equals
from, they changed state without leaving the group |
categorical |
| est |
how many people the ACS estimates made that move in the
year |
count |
| moe |
the margin of error on that estimate, at 90%
confidence |
continuous |
| cells |
how many state-to-state pairs were added together to
make this cell |
count |
| suppressed |
how many of those pairs the Census would not
release |
count |
The states are grouped into the Census Bureau’s own nine
divisions, the clusters of neighbouring states — New England,
the Middle Atlantic, the Pacific and so on — that the Bureau uses to
summarise the country, with Puerto Rico carried as a tenth group. The
Bureau’s divisions cover only the fifty states and the District of
Columbia, and 36,401 people left Puerto Rico for a state that year. The
list of which state belongs to which division is the one this book’s regional-shift
brief uses, checked there against the Bureau’s published region
totals for every decade since 1910.
| Northeast |
Middle Atlantic |
3 |
42,020,276 |
55 |
| Northeast |
New England |
6 |
15,250,253 |
21 |
| Midwest |
East North Central |
5 |
47,144,543 |
62 |
| Midwest |
West North Central |
7 |
21,736,206 |
29 |
| South |
East South Central |
4 |
19,706,473 |
26 |
| South |
South Atlantic |
9 |
68,975,950 |
85 |
| South |
West South Central |
4 |
42,594,264 |
53 |
| West |
Mountain |
8 |
25,891,835 |
33 |
| West |
Pacific |
5 |
53,316,668 |
71 |
| Puerto Rico |
Puerto Rico |
1 |
3,188,457 |
0 |
The grouping is a decision, not a fact about the country. The
Bureau fixed these divisions in 1910. They put Delaware and
Florida in one group, Maryland in the South, Missouri in the Midwest,
and Texas with Arkansas and Oklahoma. Every sentence below about “the
South” is a sentence about that list of states, and a different list
would draw a different circle from identical data.
Two cleaning decisions travel with the grouping, and both push in a
known direction. First, 279 of the 2,652 state pairs are not
published at all: the Bureau releases no estimate when too few
sampled households made a move. Aggregation adds them as zeros, because
there is nothing else to add, so the group totals run slightly low.
matrix.csv therefore carries a count of suppressed pairs in
every cell, and 78 of the 99 division-to-division cells contain at least
one. A cell assembled mostly out of suppressed pairs cannot pass itself
off as a measurement.
Second, margins of error on the grouped cells are added in
quadrature, which is the Bureau’s own instruction for a sum of
published estimates: square each margin, add the squares, and
take the square root of the total. The largest exchange in the country
shows the arithmetic. Middle Atlantic to South Atlantic carries a margin
of ±16,182, and the return flow ±13,094. The net between them is the
difference of the two estimates, and its margin is the square root of
16,182² plus 13,094², which comes to ±20,816 — less than the two added
outright, because two errors are unlikely to both fall the same way.
That rule assumes the errors are independent, and cells from a single
survey are not quite independent. So the margins below are approximate,
and if they are wrong they are too small.
Before you read on, commit to a number. Roughly 7.2
million Americans changed state in a year. What share of them do
you think crossed a Census division boundary — left the
Northeast for the South, say — rather than moving to a neighbouring
state inside the same division? Write down a percentage.
What it says about democracy
Figure 1. A year of interstate migration, 2024. A
chord diagram fits because the data is a square grid of flows among the
same ten groups, and the circle is the one form that shows every pair at
once. Each rim segment is one division, sized by how many people left
it. A ribbon’s width where it meets the rim is how many people that
division sent, so the taper of a ribbon is the net
flow; ribbons take the colour of whichever division sent more.
Click a rim segment to isolate it; the buttons switch to the four-region
grouping and drop the within-division ribbons.
Now the prediction. 26.9% of interstate moves do not cross a
division boundary. Of 7,188,344 moves in the grid, 1,935,522
were to another state in the same division: New York to New Jersey,
Virginia to Maryland, Ohio to Michigan. They are the fat lens-shaped
ribbons sitting on the rim in Figure 1. The button that hides them is
worth pressing twice, because with them gone the circle looks busier and
the country looks more mobile than it is.
That is the first thing the grouping does. Every one of those moves
was a real change of state, in a matrix built to record changes of
state, and grouping turns them into a shape that reads as staying
put.
The second finding is what the taper of the ribbons is showing, and
it is the answer to the exodus story.
| Middle Atlantic – South Atlantic |
307,170 |
186,857 |
494,027 |
120,313 |
20,816 |
24.4% |
yes |
| Mountain – Pacific |
169,545 |
270,712 |
440,257 |
101,167 |
18,258 |
23.0% |
yes |
| East North Central – South Atlantic |
179,787 |
158,068 |
337,855 |
21,719 |
15,812 |
6.4% |
yes |
| South Atlantic – West South Central |
161,793 |
158,255 |
320,048 |
3,538 |
20,543 |
1.1% |
no |
| South Atlantic – Pacific |
123,341 |
173,769 |
297,110 |
50,428 |
15,856 |
17.0% |
yes |
| South Atlantic – East South Central |
132,019 |
121,171 |
253,190 |
10,848 |
15,231 |
4.3% |
no |
| West South Central – Pacific |
91,299 |
131,305 |
222,604 |
40,006 |
14,087 |
18.0% |
yes |
| South Atlantic – Mountain |
98,753 |
113,760 |
212,513 |
15,007 |
14,798 |
7.1% |
yes |
The largest exchange in the country is Middle Atlantic with South
Atlantic: 307,170 people one way, 186,857 back, 494,027 in total and a
net of 120,313. That net is the exception that stands. It is 24.4% of
the exchange, comfortably clear of its margin, and it is the
most directional big exchange in the country. Even here, 75.6%
of the movement between the two divisions cancelled out.
The typical case cancels harder. Across all 45 pairs of
divisions the median net is 12.1% of the gross flow, and adding
every pair together gives the same answer: 12.6% of all movement between
divisions is net. The other 87.4% is two people passing each other in
opposite directions. Middle Atlantic and Pacific exchanged 133,689
people for a net of 179, against a margin of 9,506, which is
statistically nothing. South Atlantic and West South Central exchanged
320,048 people, a third of a million, for a net of 3,538 with a margin
of 20,543.
Only 21 of the 45 division pairs have a net larger than its
own margin of error. Group up to the four regions and it is 6
of 10. A net is a difference between two survey estimates and inherits
the uncertainty of both, which is why a net of twenty thousand people
can be indistinguishable from zero.
Figure 2. The same matrix, as a matrix. Thousands of
people moving from the row’s division to the column’s, shaded on a log
scale, so each step of shading is a tenfold increase rather than a fixed
number of people; the diagonal is moves that changed state without
leaving the division. Hover any cell for the estimate, its margin of
error, and how many suppressed state pairs are inside it. The button
switches to net flow, and blanks every pair whose net is smaller than
its own margin of error.
Press it. Most of the matrix goes blank, and what is
left is a small number of genuinely directional exchanges sitting in a
field of churn. That is the honest picture of American migration, and no
chord diagram can draw it, because a ribbon has no way to say this
taper is not distinguishable from parallel. The trade runs the
other way too: the matrix cannot show at a glance that the Pacific
division sends people almost everywhere while East South Central mostly
trades with its neighbours. Figure 1 hands you that in a second and will
not surrender a single value.
The regions hold one more exception worth telling. The
Northeast-to-South net, 200,547 people out of 833,537 exchanged, runs
the way the Sun Belt story says. But the South and the West exchanged
1,042,385 people, and their net of 141,743 ran toward the West,
which is not the direction the story predicts. The button on Figure 1
will show you both.
Why does any of this matter to democracy? Because House seats are
apportioned by population, and population moves.
| East South Central |
473,482 |
389,310 |
+84,172 |
4.27 |
26 |
| Mountain |
827,891 |
735,394 |
+92,497 |
3.57 |
33 |
| South Atlantic |
1,901,317 |
1,661,721 |
+239,596 |
3.47 |
85 |
| West South Central |
801,009 |
696,509 |
+104,500 |
2.45 |
53 |
| West North Central |
488,769 |
493,085 |
-4,316 |
-0.20 |
29 |
| New England |
377,932 |
385,241 |
-7,309 |
-0.48 |
21 |
| East North Central |
790,360 |
833,263 |
-42,903 |
-0.91 |
62 |
| Puerto Rico |
22,456 |
36,401 |
-13,945 |
-4.37 |
0 |
| Pacific |
830,562 |
1,070,577 |
-240,015 |
-4.50 |
71 |
| Middle Atlantic |
674,566 |
886,843 |
-212,277 |
-5.05 |
55 |
The 5 divisions losing people on net hold 238 House seats between
them; the 4 gaining hold 197. Middle Atlantic loses 5.0 people per
thousand residents a year and East South Central gains 4.3, and a decade
of that is what the apportionment brief
is recomputing when the seat totals change. The rates are small, and
that is the point worth carrying away. Nothing in Figure 1 looks like an
exodus, yet a net flow of a few people per thousand per year, sustained
for a decade, reorganises the House of Representatives. That is why this
table is published annually and read cumulatively.
What this brief cannot tell you
Anything the grouping did not decide first. Nine
divisions is 99 ribbons; fifty-two units would be 2,652 and unreadable.
Every finding above would change under a different list: how much
cancels, which pairs stand out, what counts as “within”. The Census
divisions are a 1910 committee decision, not a natural kind, and a
grouping by metropolitan area or by cost of living would draw a
different circle from identical numbers.
A trend. This is a single ACS release. The 26.9% of
moves that stay inside a division and the 12.1% median net are one
year’s estimates. The migration brief carries the
long series, in which American mobility has been falling for
decades.
The suppressed cells. The 279 missing state pairs
were added as zeros, and they are the smallest flows between the
smallest states, so the rim segments for the least populated divisions
are the least trustworthy. They cannot be recovered from the published
state totals either, because the ACS estimates its cells and its totals
separately and they do not add up.
Why anybody moved, or whether they moved back.
Somebody who left Pennsylvania for Florida and returned the next year
appears twice, in opposite directions, and contributes nothing to any
net. That is not an error in the data; it is what the data is. The word
for it is churn, and it is 87.9% of what the median pair of divisions
did to each other.
What you should have learned
- 26.9% of interstate moves never cross a division
boundary, so a circle drawn from nine groups reads as staying
put even though every one of its 7,188,344 moves changed state.
Aggregation is a decision with consequences, made before the first pixel
is drawn.
- Migration is mostly churn: across the 45 division pairs the median
net is 12.1% of the gross flow, and only 12.6% of all between-division
movement is net.
- Only 21 of the 45 division nets, and 6 of the 10 region nets, are
larger than their own margins of error, because a net inherits the
uncertainty of both estimates it is built from.
- The one-way exodus is the exception, not the rule: Middle
Atlantic–South Atlantic is the most directional large exchange in the
country, and even there 75.6% of the movement cancelled.
- A chord diagram shows the shape of a whole flow grid at a glance and
will not surrender a number; the matrix does the opposite. Neither
replaces the other.
Extensions
pairs.csv has a_to_b, b_to_a,
gross, net and net_pct_of_gross.
Sort by the last one. Which pairs are a genuine one-way move, and which
are two large flows that almost cancel?- Count the TRUE rows in the
net_sig column of
pairs.csv. What is left of the story about Americans moving
between regions once the nets that cannot be told apart from zero are
set aside?
matrix.csv records how many state pairs were
suppressed in each cell. Does suppression fall evenly
across the grid, or does it land on particular kinds of place?states.csv maps each state to both a
division and a region. Regroup the flows by
region and compare: does the picture change, and would you have known if
you had only ever seen one grouping?- Stretch. Download the previous year’s release of
the same Bureau table, from the address in the sources below with the
year changed, and rebuild the division pairs. Do the same nets clear
their margins, or does the set churn?
- Stretch. Invent a grouping of your own, by which
party carried the state or by cost of living, and reaggregate the state
flows in a spreadsheet using your list. Does the exodus story look
stronger or weaker than under the Bureau’s 1910 map?
Sources
Data
Academic literature
- Krzywinski, Martin et al. (2009). “Circos: an information aesthetic
for comparative genomics.” Genome Research 19(9): 1639–1645.
The paper that made the chord diagram a standard form, and the source of
the layout in Figure 1. https://pmc.ncbi.nlm.nih.gov/articles/PMC2752132/
The data itself
Every figure above is drawn from these tables. They are plain CSV,
they open in a spreadsheet, and they are yours to take further.
arcs.csv, groups.csv, matrix.csv, pairs.csv, states.csv
One more file is not data about the subject – it is how this chapter
checked its own numbers: facts.csv, the individual
numbers the text above quotes.
