Do all the roads lead to Rome?

Did Romans found their empire's cities — or just move into them? Mostly move in. The foundation-nation layer shows most cities were ancient long before Rome arrived: Dorians, Ionians, Etruscans, Phoenicians and other peoples settled the map first, and named founders — Romulus and Remus, Philip II of Macedon, Seleucus I Nicator — stand behind many famous sites. Only cities whose founding date falls after Roman conquest are flagged as Roman colonies or refoundations. Rome didn't found the ancient world; it acquired it.

Were Roman cities so brilliant — or just impossible to kill? Both. 122 Roman sites still carry a living successor of 100,000+ people — Londinium/London, Lutetia/Paris, Mediolanum/Milan, Byzantium/Istanbul — and 80% of all catalogued cities lay within 5 km of a road. The survival is real, but it cuts both ways: Rome itself held ~923,000 people c. AD 165 and houses ~3,600,000 today, while Londinium's ~38,000 became ~10,500,000. The network chose the spots; the following two millennia did the compounding.

Did all roads lead to Rome — or was there another connectivity pattern? The proverb holds at the top: Rome's hexagon ranks #1 on both degree and km-weighted betweenness. But the through-traffic belonged to corridor cities — Aquileia and Concordia (26.7%), the Philippopolis–Hadrianopolis–Byzantium chain, Sirmium, Nicomedia — while terminal capitals such as Rome, York and Carthage carry almost none. One network, many hubs: betweenness measures position on paths, not importance.

1. Network. The DARMC Roman Road Network (2008) shapefile (7,154 segments, Lambert Conformal Conic) is reprojected to EPSG:4326; an undirected graph joins segment endpoints (5,086 nodes / 7,048 edges).

2. Centrality. Degree and unnormalized km-weighted betweenness centrality per node (edge lengths as path costs), aggregated into H3 hexagons (resolution 3) covering the Empire's extent (20 km buffer). Rome's hexagon ranks #1 on both measures.

3. Cities. Hanson 2016 catalogue (1,388 cities): road access via nearest-road distance in the metric CRS; Wikipedia links resolved per ancient city (disambiguation-aware); founders from Wikidata P112 with a pre-Roman regional-power fallback and curated overrides; Greek tribes distinguished (Dorian/Ionian/Achaean/Aeolian/Macedonian…).

3a. Empire ranking. Each city carries a Barrington Atlas Rank: 1 = largest (Rome-scale metropolis, 14 cities), 2 = major (162), 3 = significant (816), 4–5 = minor (unranked entries count as 5). The map's "Empire ranking" scheme colors every city by this scale — a size grading from the Barrington Atlas of the Greek and Roman World, independent of the population estimates in step 4.

4. Population. 210 direct estimates from Hanson & Ortman 2017 (JRSI); a density relation calibrated on their data (pop = 44.5 × area^1.33, r² = 0.985) converts the 885 measured built-up areas; Chandler/Modelski (Reba et al. 2016) fills remaining majors at AD 100–200. All estimates share one time window.

5. Urban Network Analysis (City Form Lab methodology). The roads are planarized (split at every crossing) and contracted to junctions; cities are population-weighted nodes. Weighted betweenness = share of population-weighted shortest paths through a city, with every tied shortest path counted fractionally (exact Brandes accumulation); reach (100 km) = city population within 100 network-km. Road chunks are colored by the load they carry.

6. Capitals ×2. Two curated sets — 11 imperial capitals/residences (Rome, Constantinople, Nicomedia, Milan, Ravenna, Trier, Sirmium, Antioch, Thessalonica, York, Serdica) and 47 with provincial capitals added (Lugdunum, Ephesus, Corduba, Londinium…) — each run as its own variant with capital node weight = population × 2, shown as separate map layers. Populations are AD 100–165 while most imperial capitals are 284–476: a deliberate anachronism modelling administrative pull across the imperial era.

7. Alive today. The Reba/Reitsma/Seto 2016 city datasets (Chandler + Modelski, populations up to AD 1975) supply each modern city's latest population. Every modern city of 100,000+ within 15 km of a Roman site pins that site (nearest wins; last estimate must be post-1800, so dead cities like Ephesus or Thebes drop out): 122 Roman cities — Londinium/London, Lutetia/Paris, Mediolanum/Milan, Roma, Byzantium/Istanbul… — carry a living successor, shown as cyan rings sized by the modern population. Where the Reba trail is stale (Tarragona absent; Córdoba, Ljubljana, İzmir last estimated below 100k) a curated supplement (data/modern_cities_extra.csv, recent city-proper censuses) fills the gap — 60 sites.

• Via Rome's hexagon tops both degree and km-weighted betweenness — the network data agrees with the proverb.
• Via Damascus, Byzantium, Milan, Lepcis Magna and Lyon sit directly on a digitized road (<0.1 km); Carthage, Jerusalem, Alexandria, Athens and London connect within 2 km.
• Via The unconnected majors cluster in Crete and the Peloponnesian interior — a digitization gap in the DARMC layer, not an ancient reality.
• Via Exact tie-splitting (every tied shortest path counted fractionally) lowers the corridor shares: Aquileia/Concordia lead at 26.7%/26.6%, then the Philippopolis–Hadrianopolis–Byzantium corridor — the empire's one-bridge-per-region bottlenecks.
• Via Capitals that lie on corridors carry heavy through-traffic (Sirmium 21.9%, Byzantium 22.9%, Ravenna 18.3%, Nicomedia 21.7%), while terminal capitals — Rome, York, Carthage, Ephesus — carry almost none: betweenness measures position on paths, not importance.
• Via Boosting all 46 capitals pulls western traffic onto the transalpine and Asia Minor routes: Nicaea and Nicomedia enter the top ten (20.8% / 20.6%).