dorsal/arxiv
View SchemaAccelerating, hyper-accelerating, and decelerating probabilistic networks
| Authors | M. J. Gagen, J. S. Mattick |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0502013 |
| URL | https://arxiv.org/abs/q-bio/0502013 |
| DOI | 10.1103/PhysRevE.72.016123 |
| Journal | Physical Review E, 72, 016123 (2005) |
Abstract
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyper-accelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.
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"abstract": "Many growing networks possess accelerating statistics where the number of\nlinks added with each new node is an increasing function of network size so the\ntotal number of links increases faster than linearly with network size. In\nparticular, biological networks can display a quadratic growth in regulator\nnumber with genome size even while remaining sparsely connected. These features\nare mutually incompatible in standard treatments of network theory which\ntypically require that every new network node possesses at least one\nconnection. To model sparsely connected networks, we generalize existing\napproaches and add each new node with a probabilistic number of links to\ngenerate either accelerating, hyper-accelerating, or even decelerating network\nstatistics in different regimes. Under preferential attachment for example,\nslowly accelerating networks display stationary scale-free statistics\nrelatively independent of network size while more rapidly accelerating networks\ndisplay a transition from scale-free to exponential statistics with network\ngrowth. Such transitions explain, for instance, the evolutionary record of\nsingle-celled organisms which display strict size and complexity limits.",
"arxiv_id": "q-bio/0502013",
"authors": [
"M. J. Gagen",
"J. S. Mattick"
],
"categories": [
"q-bio.MN",
"q-bio.QM"
],
"doi": "10.1103/PhysRevE.72.016123",
"journal_ref": "Physical Review E, 72, 016123 (2005)",
"title": "Accelerating, hyper-accelerating, and decelerating probabilistic networks",
"url": "https://arxiv.org/abs/q-bio/0502013"
},
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