TY - JOUR

T1 - RAGE - A rapid graphlet enumerator for large networks

AU - Marcus, D.

AU - Shavitt, Y.

N1 - Funding Information:
This work was partially funded by the Israeli Science Foundation’s center of knowledge grant 1685/07.

PY - 2012/2/2

Y1 - 2012/2/2

N2 - Counting network graphlets (and motifs) was shown to have an important role in studying a wide range of complex networks. However, when the network size is large, as in the case of the Internet topology and WWW graphs, counting the number of graphlets becomes prohibitive for graphlets of size 4 and above. Devising efficient graphlet counting algorithms thus becomes an important goal. In this paper, we present efficient counting algorithms for 4-node graphlets. We show how to efficiently count the total number of each type of graphlet, and the number of graphlets adjacent to a node. We further present a new algorithm for node position-aware graphlet counting, namely partitioning the graphlet count by the node position in the graphlet. Since our algorithms are based on non-induced graphlet count, we also show how to calculate the count of induced graphlets given the non-induced count. We implemented our algorithms on a set of both synthetic and real-world graphs. Our evaluation shows that the algorithms are scalable and perform up to 30 times faster than the state-of-the-art. We then apply the algorithms on the Internet Autonomous Systems (AS) graph, and show how fast graphlet counting can be leveraged for efficient and scalable classification of the ASes that comprise the Internet. Finally, we present RAGE, a tool for rapid graphlet enumeration available online.

AB - Counting network graphlets (and motifs) was shown to have an important role in studying a wide range of complex networks. However, when the network size is large, as in the case of the Internet topology and WWW graphs, counting the number of graphlets becomes prohibitive for graphlets of size 4 and above. Devising efficient graphlet counting algorithms thus becomes an important goal. In this paper, we present efficient counting algorithms for 4-node graphlets. We show how to efficiently count the total number of each type of graphlet, and the number of graphlets adjacent to a node. We further present a new algorithm for node position-aware graphlet counting, namely partitioning the graphlet count by the node position in the graphlet. Since our algorithms are based on non-induced graphlet count, we also show how to calculate the count of induced graphlets given the non-induced count. We implemented our algorithms on a set of both synthetic and real-world graphs. Our evaluation shows that the algorithms are scalable and perform up to 30 times faster than the state-of-the-art. We then apply the algorithms on the Internet Autonomous Systems (AS) graph, and show how fast graphlet counting can be leveraged for efficient and scalable classification of the ASes that comprise the Internet. Finally, we present RAGE, a tool for rapid graphlet enumeration available online.

KW - Efficient algorithms

KW - Graphlets

KW - Network motifs

KW - Subgraph enumeration

UR - http://www.scopus.com/inward/record.url?scp=84856046088&partnerID=8YFLogxK

U2 - 10.1016/j.comnet.2011.08.019

DO - 10.1016/j.comnet.2011.08.019

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84856046088

SN - 1389-1286

VL - 56

SP - 810

EP - 819

JO - Computer Networks

JF - Computer Networks

IS - 2

ER -