Search results for: cliques

Authors: A. Melka, N. Slater, A. Mualem, Y. Louzoun

Abstract:

Networks are often presented as containing a “core” and a “periphery.” The existence of a core suggests that some vertices are central and form the skeleton of the network, to which all other vertices are connected. An alternative view of graphs is through communities. Multiple measures have been proposed for dense communities in graphs, the most classical being k-cliques, k-cores, and k-plexes, all presenting groups of tightly connected vertices. We here show that the edge number thresholds for such communities to emerge and for their percolation into a single dense connectivity component are very close, in all networks studied. These percolating cliques produce a natural core and periphery structure. This result is generic and is tested in configuration models and in real-world networks. This is also true for k-cores and k-plexes. Thus, the emergence of this connectedness among communities leading to a core is not dependent on some specific mechanism but a direct result of the natural percolation of dense communities.

Keywords: Networks, cliques, percolation, core structure, phase transition.

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Authors: Eleftheria Tzamali, Panayiota Poirazi, Ioannis G. Tollis, Martin Reczko

Abstract:

Stable bacterial polymorphism on a single limiting resource may appear if between the evolved strains metabolic interactions take place that allow the exchange of essential nutrients [8]. Towards an attempt to predict the possible outcome of longrunning evolution experiments, a network based on the metabolic capabilities of homogeneous populations of every single gene knockout strain (nodes) of the bacterium E. coli is reconstructed. Potential metabolic interactions (edges) are allowed only between strains of different metabolic capabilities. Bacterial communities are determined by finding cliques in this network. Growth of the emerged hypothetical bacterial communities is simulated by extending the metabolic flux balance analysis model of Varma et al [2] to embody heterogeneous cell population growth in a mutual environment. Results from aerobic growth on 10 different carbon sources are presented. The upper bounds of the diversity that can emerge from single-cloned populations of E. coli such as the number of strains that appears to metabolically differ from most strains (highly connected nodes), the maximum clique size as well as the number of all the possible communities are determined. Certain single gene deletions are identified to consistently participate in our hypothetical bacterial communities under most environmental conditions implying a pattern of growth-condition- invariant strains with similar metabolic effects. Moreover, evaluation of all the hypothetical bacterial communities under growth on pyruvate reveals heterogeneous populations that can exhibit superior growth performance when compared to the performance of the homogeneous wild-type population.

Keywords: Bacterial polymorphism, clique identification, dynamic FBA, evolution, metabolic interactions.

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