39 research outputs found
Latent Geometry for Complementarity-Driven Networks
Networks of interdisciplinary teams, biological interactions as well as food
webs are examples of networks that are shaped by complementarity principles:
connections in these networks are preferentially established between nodes with
complementary properties. We propose a geometric framework for
complementarity-driven networks. In doing so we first argue that traditional
geometric representations, e.g., embeddings of networks into latent metric
spaces, are not applicable to complementarity-driven networks due to the
contradiction between the triangle inequality in latent metric spaces and the
non-transitivity of complementarity. We then propose the cross-geometric
representation for these complementarity-driven networks and demonstrate that
this representation (i) follows naturally from the complementarity rule, (ii)
is consistent with the metric property of the latent space, (iii) reproduces
structural properties of real complementarity-driven networks, if the latent
space is the hyperbolic disk, and (iv) allows for prediction of missing links
in complementarity-driven networks with accuracy surpassing existing
similarity-based methods. The proposed framework challenges social network
analysis intuition and tools that are routinely applied to
complementarity-driven networks and offers new avenues towards descriptive and
prescriptive analysis of systems in science of science and biomedicine
Long-Range Correlations and Memory in the Dynamics of Internet Interdomain Routing
Data transfer is one of the main functions of the Internet. The Internet
consists of a large number of interconnected subnetworks or domains, known as
Autonomous Systems. Due to privacy and other reasons the information about what
route to use to reach devices within other Autonomous Systems is not readily
available to any given Autonomous System. The Border Gateway Protocol is
responsible for discovering and distributing this reachability information to
all Autonomous Systems. Since the topology of the Internet is highly dynamic,
all Autonomous Systems constantly exchange and update this reachability
information in small chunks, known as routing control packets or Border Gateway
Protocol updates. Motivated by scalability and predictability issues with the
dynamics of these updates in the quickly growing Internet, we conduct a
systematic time series analysis of Border Gateway Protocol update rates. We
find that Border Gateway Protocol update time series are extremely volatile,
exhibit long-term correlations and memory effects, similar to seismic time
series, or temperature and stock market price fluctuations. The presented
statistical characterization of Border Gateway Protocol update dynamics could
serve as a ground truth for validation of existing and developing better models
of Internet interdomain routing
Cosmological networks
Networks often represent systems that do not have a long history of study in traditional fields of physics; albeit, there are some notable exceptions, such as energy landscapes and quantum gravity. Here, we consider networks that naturally arise in cosmology. Nodes in these networks are stationary observers uniformly distributed in an expanding open Friedmann-Lemaitre-Robertson-Walker universe with any scale factor and two observers are connected if one can causally influence the other. We show that these networks are growing Lorentz-invariant graphs with power-law distributions of node degrees. These networks encode maximum information about the observable universe available to a given observer
Structure of Business Firm Networks and Scale-Free Models
We study the structure of business firm networks and scale-free models with
degree distribution using the method of
-shell decomposition.We find that the Life Sciences industry network consist
of three components: a ``nucleus,'' which is a small well connected subgraph,
``tendrils,'' which are small subgraphs consisting of small degree nodes
connected exclusively to the nucleus, and a ``bulk body'' which consists of the
majority of nodes. At the same time we do not observe the above structure in
the Information and Communication Technology sector of industry. We also
conduct a systematic study of these three components in random scale-free
networks. Our results suggest that the sizes of the nucleus and the tendrils
decrease as increases and disappear for . We compare
the -shell structure of random scale-free model networks with two real world
business firm networks in the Life Sciences and in the Information and
Communication Technology sectors. Our results suggest that the observed
behavior of the -shell structure in the two industries is consistent with a
recently proposed growth model that assumes the coexistence of both
preferential and random agreements in the evolution of industrial networks
Structure of Business Firm Networks and Scale-Free Models.
We study the structure of business firm networks in the Life Sciences (LS) and the Information and Communication Technology (ICT) sectors. We analyze business firm networks and scale-free models with degree distribution P(q) proportional to (q + c)^-λ using the method of k-shell decomposition. We find that the LS network consists of three components: a "nucleus", which is a small well connected subgraph, "tendrils", which are small subgraphs consisting of small degree nodes connected exclusively to the nucleus, and a "bulk body" which consists of the majority of nodes. At the same time we do not observe the above structure in the ICT network. Our results suggest that the sizes of the nucleus and the tendrils decrease as λ increases and disappear for λ greater or equal to 3. We compare the k-shell structure of random scale-free model networks with the real world business firm networks. The observed behavior of the k-shell structure in the two industries is consistent with a recently proposed growth model that assumes the coexistence of both preferential and random regimes in the evolution of industry networks.
Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks
We study the betweenness centrality of fractal and non-fractal scale-free
network models as well as real networks. We show that the correlation between
degree and betweenness centrality of nodes is much weaker in fractal
network models compared to non-fractal models. We also show that nodes of both
fractal and non-fractal scale-free networks have power law betweenness
centrality distribution . We find that for non-fractal
scale-free networks , and for fractal scale-free networks , where is the dimension of the fractal network. We support
these results by explicit calculations on four real networks: pharmaceutical
firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network
at AS level (N=20566), where is the number of nodes in the largest
connected component of a network. We also study the crossover phenomenon from
fractal to non-fractal networks upon adding random edges to a fractal network.
We show that the crossover length , separating fractal and
non-fractal regimes, scales with dimension of the network as
, where is the density of random edges added to the network.
We find that the correlation between degree and betweenness centrality
increases with .Comment: 19 pages, 6 figures. Submitted to PR
Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks
We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution P(C) ~ C^δ. We find that for non-fractal scale-free networks δ = -2, and for fractal scale-free networks δ = -2 + 1/dB, where dB is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N = 6776), yeast (N = 1458), WWW (N = 2526), and a sample of Internet network at AS level (N = 20566), where N is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length ℓ*, separating fractal and non-fractal regimes, scales with dimension dB of the network as p−1/dB, where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p.Interfirm networks; R&D collaborations, Pharmaceutical industry; ICT.
Hidden Variables in Bipartite Networks
We introduce and study random bipartite networks with hidden variables. Nodes
in these networks are characterized by hidden variables which control the
appearance of links between node pairs. We derive analytic expressions for the
degree distribution, degree correlations, the distribution of the number of
common neighbors, and the bipartite clustering coefficient in these networks.
We also establish the relationship between degrees of nodes in original
bipartite networks and in their unipartite projections. We further demonstrate
how hidden variable formalism can be applied to analyze topological properties
of networks in certain bipartite network models, and verify our analytical
results in numerical simulations
Topological properties and organizing principles of semantic networks
Interpreting natural language is an increasingly important task in computer
algorithms due to the growing availability of unstructured textual data.
Natural Language Processing (NLP) applications rely on semantic networks for
structured knowledge representation. The fundamental properties of semantic
networks must be taken into account when designing NLP algorithms, yet they
remain to be structurally investigated. We study the properties of semantic
networks from ConceptNet, defined by 7 semantic relations from 11 different
languages. We find that semantic networks have universal basic properties: they
are sparse, highly clustered, and many exhibit power-law degree distributions.
Our findings show that the majority of the considered networks are scale-free.
Some networks exhibit language-specific properties determined by grammatical
rules, for example networks from highly inflected languages, such as e.g.
Latin, German, French and Spanish, show peaks in the degree distribution that
deviate from a power law. We find that depending on the semantic relation type
and the language, the link formation in semantic networks is guided by
different principles. In some networks the connections are similarity-based,
while in others the connections are more complementarity-based. Finally, we
demonstrate how knowledge of similarity and complementarity in semantic
networks can improve NLP algorithms in missing link inference
Stability of a Giant Connected Component in a Complex Network
We analyze the stability of the network's giant connected component under
impact of adverse events, which we model through the link percolation.
Specifically, we quantify the extent to which the largest connected component
of a network consists of the same nodes, regardless of the specific set of
deactivated links. Our results are intuitive in the case of single-layered
systems: the presence of large degree nodes in a single-layered network ensures
both its robustness and stability. In contrast, we find that interdependent
networks that are robust to adverse events have unstable connected components.
Our results bring novel insights to the design of resilient network topologies
and the reinforcement of existing networked systems