Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles Export

@article{citeulike:6100480, abstract = {Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, we study a model where clustering is enhanced by means of a fugacity term as in the Strauss (or "triangle") model, but where the degree sequence is strictly preserved -- thus maintaining the quenched heterogeneity of nodes found in the original degree sequence. Similar models had been proposed previously in [R. Milo et al., Science 298, 824 (2002)]. We find that our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree k \> 2 we find a single first order transition. For all non-regular networks that we studied (including Erdos - Renyi and scale-free networks) we find multiple jumps resembling first order transitions, together with strong hysteresis. The latter transitions are driven by the sudden emergence of "cluster cores": groups of highly interconnected nodes with higher than average degrees. To study these cluster cores visually, we introduce q-clique adjacency plots. We find that these cluster cores constitute distinct communities which emerge spontaneously from the triangle generating process. Finally, we point out that cluster cores produce pitfalls when using the present (and similar) models as null models for strongly clustered networks, due to the very strong hysteresis which effectively leads to broken ergodicity on realistic time scales.}, archivePrefix = {arXiv}, author = {Foster, David V. and Foster, Jacob G. and Paczuski, Maya and Grassberger, Peter}, citeulike-article-id = {6100480}, citeulike-linkout-0 = {http://arxiv.org/abs/0911.2055}, citeulike-linkout-1 = {http://arxiv.org/pdf/0911.2055}, day = {11}, eprint = {0911.2055}, keywords = {network\_sampling, networks}, month = {Nov}, posted-at = {2009-11-12 03:54:30}, priority = {2}, title = {Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles}, url = {http://arxiv.org/abs/0911.2055}, year = {2009} }

TY - JOUR ID - citeulike:6100480 L3 - citeulike-article-id:6100480 N2 - Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, we study a model where clustering is enhanced by means of a fugacity term as in the Strauss (or "triangle") model, but where the degree sequence is strictly preserved -- thus maintaining the quenched heterogeneity of nodes found in the original degree sequence. Similar models had been proposed previously in [R. Milo et al., Science 298, 824 (2002)]. We find that our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree k > 2 we find a single first order transition. For all non-regular networks that we studied (including Erdos - Renyi and scale-free networks) we find multiple jumps resembling first order transitions, together with strong hysteresis. The latter transitions are driven by the sudden emergence of "cluster cores": groups of highly interconnected nodes with higher than average degrees. To study these cluster cores visually, we introduce q-clique adjacency plots. We find that these cluster cores constitute distinct communities which emerge spontaneously from the triangle generating process. Finally, we point out that cluster cores produce pitfalls when using the present (and similar) models as null models for strongly clustered networks, due to the very strong hysteresis which effectively leads to broken ergodicity on realistic time scales. TI - Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles KW - network_sampling KW - networks AU - Foster, David AU - Foster, Jacob AU - Paczuski, Maya AU - Grassberger, Peter PY - 2009/Nov/11/ UR - http://arxiv.org/abs/0911.2055 ER -