## Application of Modern Network Theory to Analysis of Complex Systems |

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applied arbitrarily basis set characteristics chord Circuit based column matrix complement complementary complex systems constant flow constant pressure elements constant pressure pumps coordinate system dashpot device element digital computer technology directed graph direction electrical engineering Electrical Network electromechanical system element disjoint elements or devices end elements end vertex finite set force meter graph G Graph Theory hydraulic system ical incident interconnected Kirchhoff's law length Lewis Research Center line segment linear mechanical subsystems mass matrix notation maximum number measured ments methodology mixed system MNT analysis technique Modern Network Theory Myril number of elements NUMBER OF SOLUTION number of specified orientation problem represent result seg and circuit set of elements set of segs shown in figure SOLUTION POINTS SOLUTION Y1=Y2=Y3 specified across variables specified through variables spring submatrix system variables terminal equations theorem tree variable pairs variables associated variables of MNT vertices voltage X2 XI yx(t zero