Unicyclic Networks: Compatibility and Enumeration

Networks and compatibility: Implications for antitrust

In this paper we draw crucial parallels between the concepts of compatibility and networks and the more traditional concepts of complementarity and vertical relationships. We also develop the important distinctions between 'two-way networks' and 'one-way networks'. We then apply our framework to a number of current antitrust issues.

Compatibility and the Creation of Shared Networks

Coherence and Compatibility of Markov Logic Networks

Markov logic is a robust approach for probabilistic relational knowledge representation that uses a log-linear model of weighted first-order formulas for probabilistic reasoning. This loglinear model always exists but may not represent the knowledge engineer’s intentions adequately. In this paper, we develop a general framework for measuring this coherence of Markov logic networks by comparing ...

One-Way Networks, Two-Way Networks,Compatibility, and Public Policy

This paper develops some important concepts with respect to networks and compatibility. We note that the familiar concept of complementarity lies at the heart of the concept of compatibility. We further note the distinction between two-way networks (e.g., telephones, railroads, the Internet) and one-way networks (e.g., ATMs, television, distribution and service networks). In the former, additio...

On Unicyclic Reflexive Graphs

If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...