Geographic Graph

In the geographic model, we use the 50 largest metropolitan areas as node locations. We then divide the US continent into 5 regions, namely northeast, northcentral, southeast, southcentral and west, and categorize nodes into regions with a certain amount of overlap. Unlike the random graph model where all networks share the same geometric space, the geographic model consists of two types of networks: regional networks and national networks. Each city joins the network with probability $N_p$: the selection of nodes for a regional network considers only nodes that belong to that region; while a national network considers all 50 cities. As before, we interconnect two networks with probability $\tx_p$. The values of $\tx_p$ may be different depending on the types of the two networks. For example, two national networks will have $\tx_p = 1$, since they are almost always interconnected; while two regional networks are less likely to peer with each other directly but to transit through a national network. We allow interconnections only if two network nodes are in the same city and use $\tx_{ds}$ to decide the number of peering points of two networks.

Geographic Categorization of Metropolitan Areas

Region north_central[17] =	"Chicago, IL",	"Detroit, MI",	"Cleveland, OH",
	"Minneapolis, MN",	"St. Louis, MO",	"Denver, CO",
	"Cincinnati, OH",	"Kansas City, MO",	"Milwaukee, WI",
	"Indianapolis, IN",	"Columbus, OH",	"Salt Lake City, UT",
	"Nashville, TN",	"Memphis, TN",	"Oklahoma City, OK",
	"Grand Rapids, MI",	"Louisville, KY" ;
Region north_east[21] =	"New York, NY",	"Chicago, IL",	"Washington, DC",
	"Philadelphia, PA",	"Boston, MA",	"Detroit, MI",
	"Cleveland, OH",	"Pittsburgh, PA",	"Cincinnati, OH"
	"Milwaukee, WI",	"Virginia Beach, VA"	"Indianapolis, IN",
	"Columbus, OH",	"Charlotte, NC",	"Greensboro, NC",
	"Buffalo, NY",	"Hartford, CT",	"Providence, RI",
	"Rochester, NY",	"Raleigh, NC",	"Richmond, VA" ;
Region west[10] =	"Los Angeles, CA",	"San Francisco, CA",	"Seattle, WA",
	"Phoenix, AZ",	"San Diego, CA",	"Denver, CO",
	"Portland, OR",	"Sacramento, CA",	"Las Vegas, NV",
	"Salt Lake City, UT";
Region south_central[12] =	"Dallas, TX",	"Houston, TX",	"Atlanta, GA",
	"Phoenix, AZ",	"St. Louis, MO",	"Kansas City, MO",
	"San Antonio, TX",	"New Orleans, LA",	"Nashville, TN",
	"Austin, TX",	"Memphis, TN",	"Oklahoma City, OK";
Region south_east[15] =	"Atlanta, GA",	"Miami, FL",	"St. Petersburg, FL",
	"Virginia Beach, VA",	"Orlando, FL",	"Charlotte, NC",
	"New Orleans, LA",	"Greensboro, NC",	"Nashville, TN",
	"Memphis, TN",	"Raleigh, NC",	"Jacksonville, FL",
	"West Palm Beach, FL",	"Louisville, KY",	"Richmond, VA";