### Table 3: Stability of small world topology types. SW 1. SW 2. SW 3.

### TABLE II TOPOLOGICAL CHARACTERISTICS OF SIMULATED POWER NETWORKS FROM THE PROPOSED RANDOM-TOPOLOGY MODELS AND WS- SMALL WORLD MODEL

### Table 3 demonstrates that sparse problems in this dataset have large clustering coe cients like regular graphs, but small characteristic path lengths like ran- dom graphs. They therefore have a small world topol- ogy. By comparison, dense problems from this dataset have nodes of large degree which are less clustered. Such graphs therefore have less of a small world topol- ogy. We conjecture that graphs will often start with a sparse small world topology but will become more like dense random graphs as edges added \saturate quot; the structure.

### Table 1. Characteristic path lengths, clustering coe - cients and proximity ratios for graphs studied in [Watts and Strogatz, 1998] with a small world topology. 3 Modeling a small world Watts and Strogatz propose a model for small world graphs. Starting from a regular graph, they introduce disorder into the graph by randomly rewiring each edge with probability p. If p = 0 then the graph is completely regular and ordered. If p = 1 then the graph is com- pletely random and disordered. Intermediate values of p give graphs that are neither completely regular nor com- pletely disordered. Watts and Strogatz start from a ring

### Table 3. Recommender systems research focused on discovering existing social networks. The left column contains modeling concepts, while the center column contains examples of implicit declarations of interest or connections mined from the systems in the right column. Notice that each system relies solely on structural, rather than semantic, information. Note also that the emtpy cell in the lower right hand corner of this matrix is a reflection that few systems take advantage of small-world properties.

"... In PAGE 12: ... We conclude by discussing small-worlds [118], a new class of social networks which present compellingopportunitiesfor serendipitousrecommendation. Table3 outlines the landscape of research showcased in this section. 4.... ..."

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### Table 4. Characteristic path lengths and clustering coe cients for m by m quasigroup problems. Search cost Graphs with a small world topology demonstrate that local properties (i.e. clustering) can be bad predictors

### Table 3.1: Examples from previously encountered natural network models with the values of the small-world measures listed. Note that Cr is practi- cally the density of both the corresponding Gn;m and the network in ques- tion. The calculations on the rst row are our own; the other C. elegans measurements and those of the IMDb and the Western U.S. power grid are from [134]. The measurements of a9a31a27a10a30 -domain are from [3], those of the Internet AS level are from [24], and the thesaurus measurements from [98].

2003

Cited by 7

### Table 1 Qualitative comparison among characterizations of difierent network models and empirical results on real-world networks.

2006

"... In PAGE 7: ... Thus, some (but not all) small-world networks are also scale-free. Table1 gives a qualitative summary of the various characterizations of networks described... ..."

Cited by 4

### Table 1 Qualitative comparison among characterizations of difierent network models and empirical results on real-world networks.

2006

"... In PAGE 7: ... Thus, some (but not all) small-world networks are also scale-free. Table1 gives a qualitative summary of the various characterizations of networks described... ..."

Cited by 4

### Table 1. Properties of the reference graphs of four software systems.

2003

"... In PAGE 3: ... Graph models of software systems are another example of clustered small-world graphs. Table1 shows data for reference graphs of four object-oriented programs. The nodes of the graphs are classes, and the edges are method calls, attribute usage, or inher- itance.... ..."

Cited by 5