-
3
-
-
0037174670
-
-
10.1126/science.298.5594.824
-
R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Science 298, 824 (2002). 10.1126/science.298.5594.824
-
(2002)
Science
, vol.298
, pp. 824
-
-
Milo, R.1
Shen-Orr, S.2
Itzkovitz, S.3
Kashtan, N.4
Chklovskii, D.5
Alon, U.6
-
4
-
-
1542287343
-
-
10.1126/science.1089167
-
R. Milo, S. Iztkovitz, N. Kashtan, R. Levitt, S. Shen-Orr, I. AyzenShtat, M. Sheffer, and U. Alon, Science 303, 1538 (2004). 10.1126/science.1089167
-
(2004)
Science
, vol.303
, pp. 1538
-
-
Milo, R.1
Iztkovitz, S.2
Kashtan, N.3
Levitt, R.4
Shen-Orr, S.5
Ayzenshtat, I.6
Sheffer, M.7
Alon, U.8
-
9
-
-
18744389789
-
-
10.1103/PhysRevLett.89.208701
-
M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002). 10.1103/PhysRevLett. 89.208701
-
(2002)
Phys. Rev. Lett.
, vol.89
, pp. 208701
-
-
Newman, M.E.J.1
-
11
-
-
63649127232
-
-
10.1103/PhysRevLett.102.128701
-
B. Karrer and M. E. J. Newman, Phys. Rev. Lett. 102, 128701 (2009). 10.1103/PhysRevLett.102.128701
-
(2009)
Phys. Rev. Lett.
, vol.102
, pp. 128701
-
-
Karrer, B.1
Newman, M.E.J.2
-
12
-
-
0012535670
-
-
Oxford University Press, Oxford, 10.1093/acprof:oso/9780198506263.001. 0001
-
M. Penrose, Random Geometric Graphs (Oxford University Press, Oxford, 2003). 10.1093/acprof:oso/9780198506263.001.0001
-
(2003)
Random Geometric Graphs
-
-
Penrose, M.1
-
13
-
-
42749099621
-
-
10.1103/PhysRevE.68.026121
-
M. E. J. Newman, Phys. Rev. E 68, 026121 (2003). 10.1103/PhysRevE.68. 026121
-
(2003)
Phys. Rev. e
, vol.68
, pp. 026121
-
-
Newman, M.E.J.1
-
14
-
-
33751543933
-
-
10.1103/PhysRevE.74.056114
-
M. A. Serrano and M. Boguñá, Phys. Rev. E 74, 056114 (2006). 10.1103/PhysRevE.74.056114
-
(2006)
Phys. Rev. e
, vol.74
, pp. 056114
-
-
Serrano, M.A.1
Boguñá, M.2
-
15
-
-
33751534549
-
-
10.1103/PhysRevE.74.056115
-
M. A. Serrano and M. Boguñá, Phys. Rev. E 74, 056115 (2006). 10.1103/PhysRevE.74.056115
-
(2006)
Phys. Rev. e
, vol.74
, pp. 056115
-
-
Serrano, M.A.1
Boguñá, M.2
-
18
-
-
68649124583
-
-
10.1103/PhysRevLett.103.058701
-
M. E. J. Newman, Phys. Rev. Lett. 103, 058701 (2009). 10.1103/PhysRevLett.103.058701
-
(2009)
Phys. Rev. Lett.
, vol.103
, pp. 058701
-
-
Newman, M.E.J.1
-
19
-
-
70349974267
-
-
10.1103/PhysRevE.80.036107
-
J. P. Gleeson, Phys. Rev. E 80, 036107 (2009). 10.1103/PhysRevE.80.036107
-
(2009)
Phys. Rev. e
, vol.80
, pp. 036107
-
-
Gleeson, J.P.1
-
20
-
-
70449411707
-
-
10.1103/PhysRevE.80.046121
-
J. P. Gleeson and S. Melnik, Phys. Rev. E 80, 046121 (2009). 10.1103/PhysRevE.80.046121
-
(2009)
Phys. Rev. e
, vol.80
, pp. 046121
-
-
Gleeson, J.P.1
Melnik, S.2
-
21
-
-
77549087023
-
-
10.1103/PhysRevE.80.020901
-
J. C. Miller, Phys. Rev. E 80, 020901 (2009). 10.1103/PhysRevE.80.020901
-
(2009)
Phys. Rev. e
, vol.80
, pp. 020901
-
-
Miller, J.C.1
-
24
-
-
78651435995
-
-
An exception is the geometric random graph, in which clustering occurs naturally on account of the graph's being embedded in a Euclidean space of low dimension (usually two). Geometric graphs are, however, something of a special case, most real networks having no such low-dimension embedding.
-
An exception is the geometric random graph, in which clustering occurs naturally on account of the graph's being embedded in a Euclidean space of low dimension (usually two). Geometric graphs are, however, something of a special case, most real networks having no such low-dimension embedding.
-
-
-
-
26
-
-
78651446357
-
-
One needs an additional constraint to avoid pathological graphs with two (or even more) giant components. Consider an ensemble with two subgraphs, a cycle and a clique, and assume that the probability distribution is such that a vertex participates either in cycles or in cliques but not both. Then all graphs consist of a cycle part and a clique part that are disconnected from each other, so there could be two giant components, one composed of cycles and the other composed of cliques. To avoid this pathology, we impose the restriction that one should not be able to divide the roles into two sets such that every vertex and every subgraph only have roles from one of the sets.
-
One needs an additional constraint to avoid pathological graphs with two (or even more) giant components. Consider an ensemble with two subgraphs, a cycle and a clique, and assume that the probability distribution is such that a vertex participates either in cycles or in cliques but not both. Then all graphs consist of a cycle part and a clique part that are disconnected from each other, so there could be two giant components, one composed of cycles and the other composed of cliques. To avoid this pathology, we impose the restriction that one should not be able to divide the roles into two sets such that every vertex and every subgraph only have roles from one of the sets.
-
-
-
-
27
-
-
0034323311
-
-
10.1103/PhysRevLett.85.4626
-
R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 85, 4626 (2000). 10.1103/PhysRevLett.85.4626
-
(2000)
Phys. Rev. Lett.
, vol.85
, pp. 4626
-
-
Cohen, R.1
Erez, K.2
Ben-Avraham, D.3
Havlin, S.4
-
28
-
-
4243939794
-
-
10.1103/PhysRevLett.85.5468
-
D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. 85, 5468 (2000). 10.1103/PhysRevLett.85.5468
-
(2000)
Phys. Rev. Lett.
, vol.85
, pp. 5468
-
-
Callaway, D.S.1
Newman, M.E.J.2
Strogatz, S.H.3
Watts, D.J.4
-
30
-
-
0020737985
-
-
10.1016/0025-5564(82)90036-0
-
P. Grassberger, Math. Biosci. 63, 157 (1983). 10.1016/0025-5564(82)90036- 0
-
(1983)
Math. Biosci.
, vol.63
, pp. 157
-
-
Grassberger, P.1
-
31
-
-
41349106348
-
-
10.1103/PhysRevE.66.016128
-
M. E. J. Newman, Phys. Rev. E 66, 016128 (2002). 10.1103/PhysRevE.66. 016128
-
(2002)
Phys. Rev. e
, vol.66
, pp. 016128
-
-
Newman, M.E.J.1
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