… Section 2 introduces preliminary concepts in graph theory and Shannon’s information
entropy. This section provides definitions, formulations and notation used throughout this work. …

… a formalization of concepts emerging in graph theory (especially in applications … last
inequality is assured by h ( p i ) − h ( p i − ϵ ) + h ( p j ) − h ( p j + ϵ ) ≥ 0 . To see that this inequality …

… to infer the network … inequalities to eliminate the weakest associations in every closed triplet
of nodes. Intuitively, suppose a relay of information transmission, data processing inequality …

… network inference into a graph theory framework. Figure 1 shows the workflow of a hypothetical
network … Processing Inequality. For each triplet of nodes X i , X j , and X k , the following …

… solutions on large-scale networks based on the graph theory or the complex network theory.
The FDI … It uses a triangle inequality test to recognize whether a link should be preserved or …

… Information-flow security is a critical problem today because of recent technological
developments … cameras, “loyalty” cards); networks then enable its transmission to unknown (or …

… a new method for measuring trust in social networks. In this paper, uncertainty theory is
applied to the modeling of social networks… For any feature where certain information cannot be …

… that there is a need for higher-order networks, which go beyond the paradigm of modeling
… of these recent developments. Our goals are to clarify (i) what higherorder networks are, (ii) …

… real-world networks. Therefore, simple graph theory will not suffice for examining these
networks… These limitations have led to proposing completely new statistical approaches for graph …

… and modern developments in graph theory and additive … ’s theorem, using tools from graph
theory and Fourier analysis. A key … Chapter 5 explores graph homomorphism inequalities, …