Abstract
We continue building up the information theory of non-sequential data structures such as trees, sets, and graphs. In this paper, we consider dynamic graphs generated by a full duplication model in which a new vertex selects an existing vertex and copies all of its neighbors. We ask how many bits are needed to describe the labeled and unlabeled versions of such graphs. We first estimate entropies of both versions and then present asymptotically optimal compression algorithms up to a constant term. Interestingly, for the full duplication model the labeled version needs $\Theta(n)$ bits while its unlabeled version (structure) can be described by $\Theta(\log n)$ bits due to a significant amount of symmetry $(\mathrm{i}.\mathrm{e}.$, the cardinality of the automorphism group of graphs generated by this model is on average quite high).
Highlights
Complex systems can often be modeled as dynamic graphs
Experimental results show that these variations on the duplication model better capture salient features of protein interaction networks than does the preferential attachment model [22]
In this paper we present comprehensive information-theoretic results for the full duplication model in which every new vertex is a copy of some older vertex
Summary
Complex systems can often be modeled as dynamic graphs. In these systems, patterns of interactions evolve in time, determining emergent properties, associated function, robustness, and security of the system. Due to the high power law exponent of their degree sequence (greater than 2) and lack of community structure [6], preferential attachment graphs are not likely to describe well biological networks such as protein interaction networks or gene regulatory networks [19]. For such networks another model, known as the vertex-copying model, or the duplication model, has been claimed as a better fit [25]. In Łuczak et al [17] the authors precisely analyzed the labeled and structural entropies and gave asymptotically optimal compression algorithms for preferential attachment graphs.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
