Community Core Evolution in Mobile Social Networks

<table>Two events cause the structure variation of network. (a) A link between nodes<svg height="12.4375" id="M63" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 19.424999 12.4375" width="19.424999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>and<svg height="7.9499998" id="M64" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 18.362499 7.9499998" width="18.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,7.675)"><path d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" id="x1D450"></path></g>
</svg>is added into the network because <svg height="23.174999" id="M65" style="vertical-align:-5.39578pt" version="1.1" viewbox="0 0 134.60001 23.174999" width="134.60001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,13.475,9.488)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g><g transform="matrix(.012,-0,0,-.012,13.475,21.725)"><path d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76
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<g transform="matrix(.012,-0,0,-.012,124.5,9.488)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g>
<g transform="matrix(.017,-0,0,-.017,128.663,17.65)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg>. (b) A link between nodes<svg height="12.4375" id="M66" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 20.887501 12.4375" width="20.887501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,12.162)"><path d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5
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</svg>is removed from the network because <svg height="23.174999" id="M68" style="vertical-align:-5.39578pt" version="1.1" viewbox="0 0 135.72501 23.174999" width="135.72501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>.</table>

The Scientific World Journal

Community Core Evolution in Mobile Social Networks

Figure 2