TY - GEN

T1 - Distance graphs

T2 - 5th ACM SIGACT-SIGOPS International Workshop on Foundations of Mobile Computing, DIALM-POMC

AU - Avin, Chen

PY - 2008/12/1

Y1 - 2008/12/1

N2 - We introduce and study random distance graph. A random distance, D(n,g) results from placing n points uniformly at random on the unit area disk and connecting every two points independently with probability g(d), where d is the distance between the nodes and g is the connection function. We give a connection function g(r,a,d) with parameters r and a and show the following: (a) D(n,g(r,a)) captures as special cases both the standard random geometric graph G(n,r) and the Bernoulli random graph B(n,p) (a.k.a. Erdos-Renyi graph). (b) Using results from continuum percolation we are able to bound the connectivity threshold of D(n,g(r,a)), with G(n,r) and B(n,p) as special (previously known) cases. (c) Contrary to G(n,r) and B(n,p), for a wide range of r and α a is, in fact, a "Small World" graph with high clustering coefficient of about 0.5865a and diameter of ({log n}/{log log n}). As opposed to previous Small World models that rely on deterministic sub-structures to grantee connectivity, random distance graphs offer a completely randomized model with a proved bounds for connectivity threshold, clustering coefficient and diameter.

AB - We introduce and study random distance graph. A random distance, D(n,g) results from placing n points uniformly at random on the unit area disk and connecting every two points independently with probability g(d), where d is the distance between the nodes and g is the connection function. We give a connection function g(r,a,d) with parameters r and a and show the following: (a) D(n,g(r,a)) captures as special cases both the standard random geometric graph G(n,r) and the Bernoulli random graph B(n,p) (a.k.a. Erdos-Renyi graph). (b) Using results from continuum percolation we are able to bound the connectivity threshold of D(n,g(r,a)), with G(n,r) and B(n,p) as special (previously known) cases. (c) Contrary to G(n,r) and B(n,p), for a wide range of r and α a is, in fact, a "Small World" graph with high clustering coefficient of about 0.5865a and diameter of ({log n}/{log log n}). As opposed to previous Small World models that rely on deterministic sub-structures to grantee connectivity, random distance graphs offer a completely randomized model with a proved bounds for connectivity threshold, clustering coefficient and diameter.

KW - Bernoulli graphs

KW - Connectivity

KW - Distance graphs

KW - Random geometric graphs

KW - Small world

UR - http://www.scopus.com/inward/record.url?scp=65249160516&partnerID=8YFLogxK

U2 - 10.1145/1400863.1400878

DO - 10.1145/1400863.1400878

M3 - Conference contribution

AN - SCOPUS:65249160516

SN - 9781605582443

T3 - DIALM-POMC'08: Proceedings of the ACM 5th International Workshop on Foundations of Mobile Computing

SP - 71

EP - 77

BT - DIALM-POMC'08

Y2 - 22 August 2008 through 22 August 2008

ER -